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International Journal of Research in Engineering and Science is an open access peer-reviewed international forum for scientists involved in research to publish quality and refereed papers. Papers reporting original research or experimentally proved review work are welcome. Papers for publication are selected through peer review to ensure originality, relevance, and readability.
A Moment Inequality for Overall Decreasing Life Class of Life Distributions w...inventionjournals
:A moment inequality is derived for the system whose life distribution is in an overall decreasing life (ODL) class of life distributions. A new nonparametric test statistic for testing exponentiality against ODL is investigated based on this inequality. The asymptotic normality of the proposed statistic is presented. Pitman's asymptotic efficiency, power and critical values of this test are calculated to assess the performance of the test. Real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. Wealso proposed a test for testing exponentiality versus ODL for right censored data and the power estimates of this test are also simulated for censored data for some commonly used distributions in reliability. Finally, real data are used as an example for practical problems.
The document describes an extension of Ant Colony Optimization (ACO) called ACOMV that allows it to handle mixed-variable optimization problems containing both continuous and discrete variables. ACOMV uses a solution archive, like ACOR, to probabilistically construct new solutions and guide the search. For ordered discrete variables, it uses a continuous relaxation approach by operating on the indexes of variable values rather than the values themselves. For categorical discrete variables, which have no natural ordering, it handles them natively without assumptions about ordering. The document proposes a new benchmark problem to test whether ACOMV performs better than ACOR on problems with categorical variables, since ACOR relies on ordering assumptions. Preliminary results on this benchmark and other problems are
Solution to the practice test ch 10 correlation reg ch 11 gof ch12 anovaLong Beach City College
Please Subscribe to this Channel for more solutions and lectures
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Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
Stability criterion of periodic oscillations in a (4)Alexander Decker
1) The authors establish that the distribution of the harmonic mean of group variances is a generalized beta distribution through simulation.
2) They show that the generalized beta distribution can be approximated by a chi-square distribution.
3) This means that the harmonic mean of group variances is approximately chi-square distributed, though the degrees of freedom need not be an integer. Using the harmonic mean in place of the pooled variance allows hypothesis testing when group variances are unequal.
Please Subscribe to this Channel for more solutions and lectures
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Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
The document provides information about goodness-of-fit tests and contingency tables. It defines a goodness-of-fit test as testing whether an observed frequency distribution fits a claimed distribution. It also provides the notation, requirements, and steps to conduct a goodness-of-fit test including: defining the null and alternative hypotheses, calculating the test statistic as a chi-square value, finding the critical value, and making a decision to reject or fail to reject the null hypothesis. Several examples demonstrate how to perform goodness-of-fit tests to determine if sample data fits a claimed distribution.
International Journal of Research in Engineering and Science is an open access peer-reviewed international forum for scientists involved in research to publish quality and refereed papers. Papers reporting original research or experimentally proved review work are welcome. Papers for publication are selected through peer review to ensure originality, relevance, and readability.
A Moment Inequality for Overall Decreasing Life Class of Life Distributions w...inventionjournals
:A moment inequality is derived for the system whose life distribution is in an overall decreasing life (ODL) class of life distributions. A new nonparametric test statistic for testing exponentiality against ODL is investigated based on this inequality. The asymptotic normality of the proposed statistic is presented. Pitman's asymptotic efficiency, power and critical values of this test are calculated to assess the performance of the test. Real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. Wealso proposed a test for testing exponentiality versus ODL for right censored data and the power estimates of this test are also simulated for censored data for some commonly used distributions in reliability. Finally, real data are used as an example for practical problems.
The document describes an extension of Ant Colony Optimization (ACO) called ACOMV that allows it to handle mixed-variable optimization problems containing both continuous and discrete variables. ACOMV uses a solution archive, like ACOR, to probabilistically construct new solutions and guide the search. For ordered discrete variables, it uses a continuous relaxation approach by operating on the indexes of variable values rather than the values themselves. For categorical discrete variables, which have no natural ordering, it handles them natively without assumptions about ordering. The document proposes a new benchmark problem to test whether ACOMV performs better than ACOR on problems with categorical variables, since ACOR relies on ordering assumptions. Preliminary results on this benchmark and other problems are
Solution to the practice test ch 10 correlation reg ch 11 gof ch12 anovaLong Beach City College
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
Stability criterion of periodic oscillations in a (4)Alexander Decker
1) The authors establish that the distribution of the harmonic mean of group variances is a generalized beta distribution through simulation.
2) They show that the generalized beta distribution can be approximated by a chi-square distribution.
3) This means that the harmonic mean of group variances is approximately chi-square distributed, though the degrees of freedom need not be an integer. Using the harmonic mean in place of the pooled variance allows hypothesis testing when group variances are unequal.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
The document provides information about goodness-of-fit tests and contingency tables. It defines a goodness-of-fit test as testing whether an observed frequency distribution fits a claimed distribution. It also provides the notation, requirements, and steps to conduct a goodness-of-fit test including: defining the null and alternative hypotheses, calculating the test statistic as a chi-square value, finding the critical value, and making a decision to reject or fail to reject the null hypothesis. Several examples demonstrate how to perform goodness-of-fit tests to determine if sample data fits a claimed distribution.
The Purpose of Homework Problems is Insight, Not Numbers: Crafting Exercises for an Intermediate Biological Physics Class. Bradley Roth, Oakland University. Prepared for the session "Bringing Together Biology, Medicine, and Physics in Education" at the APS March Meeting, 2020.
Bayesian Variable Selection in Linear Regression and A ComparisonAtilla YARDIMCI
In this study, Bayesian approaches, such as Zellner, Occam’s Window and Gibbs sampling, have been compared in terms of selecting the correct subset for the variable selection in a linear regression model. The aim of this comparison is to analyze Bayesian variable selection and the behavior of classical criteria by taking into consideration the different values of β and σ and prior expected levels.
The document presents two numerical methods, finite difference method (FDM) and Adomian decomposition method (ADM), for solving the Schnackenberg model, which is a system of two nonlinearly coupled reaction-diffusion equations. FDM approximates the partial derivatives in the equations with finite differences. ADM rewrites the system as an operator equation and decomposes the solution into a series. The document derives the finite difference approximations and outlines the steps of ADM. An example application is mentioned to show that ADM is more accurate and efficient than FDM for this type of problem.
Analytical Solutions of simultaneous Linear Differential Equations in Chemica...IJMERJOURNAL
ABSTRACT: Analytical method for solving homogeneous linear differential equations in chemical kinetics and pharmacokinetics using homotopy perturbation method has been proposed. The mathematical model that depicts the pharmacokinetics is solved. Herein, we report the closed form of an analytical expression for concentrations species for all values of kinetic parameters. These results are compared with numerical results and are found to be in satisfactory agreement. The obtained results are valid for the whole solution domain.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 11: Goodness-of-Fit and Contingency Tables
11.2: Contingency Tables
On Semi-Generalized Recurrent LP-Sasakian Manifoldsinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This document provides an overview of nonparametric statistical methods for analyzing ranked data. It discusses the Wilcoxon rank-sum test and sign test, which are nonparametric alternatives to the t-test that do not assume a normal distribution. The document explains how to rank data values and handle ties. It also provides examples of using the sign test to compare a sample mean to a hypothesized value and interpreting the results.
This document presents a method for calculating a cophenetic correlation coefficient for cluster analysis performed using the modified Tocher's method. The authors extend an existing algorithm to compute a cophenetic matrix based on average distances within and between clusters formed by the modified Tocher's method. They apply their method to cluster analyses of 17 garlic cultivars based on morphological characters using Mahalanobis and Euclidean distances. They compare the cophenetic correlation coefficients obtained from the modified Tocher's method to those from hierarchical clustering methods. The results demonstrate that the proposed method reliably synthesizes the original distances into cophenetic distances and obtains cophenetic correlation coefficients consistent with previous work.
Recent research in finding the optimal path by ant colony optimizationjournalBEEI
The computation of the optimal path is one of the critical problems in graph theory. It has been utilized in various practical ranges of real world applications including image processing, file carving and classification problem. Numerous techniques have been proposed in finding optimal path solutions including using ant colony optimization (ACO). This is a nature-inspired metaheuristic algorithm, which is inspired by the foraging behavior of ants in nature. Thus, this paper study the improvement made by many researchers on ACO in finding optimal path solution. Finally, this paper also identifies the recent trends and explores potential future research directions in file carving.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document discusses a one-way analysis of variance (ANOVA) used to compare the effects of different oil types (A, B, C) on car mileage. It tests the null hypothesis that the mean mileages are equal against the alternative that at least two means differ. The ANOVA calculates sums of squares and F statistics to determine if there are significant differences between the treatment means, rejecting the null hypothesis if F exceeds the critical value. If differences exist, pairwise comparisons estimate the size of differences between each pair of means using confidence intervals.
Multiple Linear Regression Model with Two Parameter Doubly Truncated New Symm...theijes
This document presents a multiple linear regression model with errors that follow a two-parameter doubly truncated new symmetric distribution. The model extends traditional linear regression by allowing for non-Gaussian distributed errors that are finite and bounded. Properties of the doubly truncated new symmetric distribution are derived, including its probability density function and characteristic function. Maximum likelihood and ordinary least squares methods are used to estimate the model parameters. A simulation study compares the proposed model to existing models that assume Gaussian or new symmetric distributed errors.
Comparison of Several Numerical Algorithms with the use of Predictor and Corr...ijtsrd
The document discusses and compares several numerical methods for solving ordinary differential equations (ODEs), including Taylor series, Runge-Kutta, Euler's method, and predictor-corrector methods. It introduces Adams-Bashforth and Milne's predictor-corrector algorithms, which use multi-step methods to iteratively predict and correct solutions. The document also covers the basic Euler's method and improved Euler's method for solving ODEs numerically through discretization.
Hopf-Bifurcation Ina Two Dimensional Nonlinear Differential EquationIJMER
This document discusses Hopf bifurcation in a two-dimensional nonlinear differential equation. It contains the following key points:
1. The paper investigates the stability of Hopf bifurcation in a two-dimensional nonlinear differential equation, finding both supercritical and subcritical Hopf bifurcation depending on parameter values.
2. The center manifold theorem and normal forms are used to study the behavior of limit cycles created or destroyed through Hopf bifurcations.
3. Hopf bifurcation refers to the creation or destruction of a periodic solution emanating from an equilibrium point as a parameter crosses a critical value. It is important for studying oscillatory behavior in nonlinear systems.
This paper considers the control problem of a class of uncertain switched systems defined on polyhedral sets known as piecewise linear systems where, instead of the conventional Caratheodory solutions, Filippov solutions are studied. In other words, in contrast to the previous studies, solutions with infinite switching in finite time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, established upon previous studies, a set of linear matrix inequalities are brought forward which determines the asymptotic stability of piecewise linear systems with Filippov solutions. Subsequently, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed H1 performance are presented. Furthermore, these results has been generalized to the case of piecewise affine systems. Finally, a V–K iteration algorithm is proposed to deal with the aforementioned bilinear matrix inequalities. The validity of the proposed method is verified through the analysis of two simulation examples.
This document discusses moments, skewness, kurtosis, and several statistical distributions including binomial, Poisson, hypergeometric, and chi-square distributions. It defines key terms such as moment ratios, central moments, theorems, skewness, kurtosis, and correlation. Properties and applications of the binomial, Poisson, and hypergeometric distributions are provided. Finally, the document discusses the chi-square test for goodness of fit and independence.
This document provides an introduction and overview to Unit 13 of the course MST209 Mathematical methods and models. Unit 13 focuses on modelling systems using non-linear differential equations. It discusses two main examples - modeling the interaction between predator and prey populations using the Lotka-Volterra equations, and modeling the motion of a pendulum using differential equations. The unit emphasizes qualitative analysis and interpretation of solutions rather than explicit solutions. It introduces concepts like equilibrium solutions and linearizing near equilibria to understand behavior. Sections 1 and 2 develop these ideas for the Lotka-Volterra population model, while Section 3 applies similar techniques to the pendulum motion model.
Eigenvalues for HIV-1 dynamic model with two delaysIOSR Journals
This document presents a new approach to solve the characteristic equation of an HIV-1 infection dynamical system with two delays. The authors develop a series expansion to approximate the eigenvalues (roots) of the nonlinear characteristic equation. They derive the characteristic equation for the linearized HIV-1 model and nondimensionalize the equation. This allows them to express the eigenvalues as a perturbation of the logarithm of a parameter and derive an equation for the perturbation term. The goal is to make the truncated series more computationally efficient for evaluating the eigenvalues.
https://utilitasmathematica.com/index.php/Index
Our Journal has recently transitioned to becoming a fully open-access journal. This transition marks a significant shift in the landscape of academic publishing, aiming to provide numerous benefits to both authors and readers. Open access has the potential to democratize knowledge, enhance research impact, and foster greater collaboration within the academic community.
Utilitas Mathematica Journal is a broad scope journal that publishes original research and review articles on all aspects of both pure and applied mathematics.The journal publishes original research in all areas of pure and applied mathematics, statistics.
The Purpose of Homework Problems is Insight, Not Numbers: Crafting Exercises for an Intermediate Biological Physics Class. Bradley Roth, Oakland University. Prepared for the session "Bringing Together Biology, Medicine, and Physics in Education" at the APS March Meeting, 2020.
Bayesian Variable Selection in Linear Regression and A ComparisonAtilla YARDIMCI
In this study, Bayesian approaches, such as Zellner, Occam’s Window and Gibbs sampling, have been compared in terms of selecting the correct subset for the variable selection in a linear regression model. The aim of this comparison is to analyze Bayesian variable selection and the behavior of classical criteria by taking into consideration the different values of β and σ and prior expected levels.
The document presents two numerical methods, finite difference method (FDM) and Adomian decomposition method (ADM), for solving the Schnackenberg model, which is a system of two nonlinearly coupled reaction-diffusion equations. FDM approximates the partial derivatives in the equations with finite differences. ADM rewrites the system as an operator equation and decomposes the solution into a series. The document derives the finite difference approximations and outlines the steps of ADM. An example application is mentioned to show that ADM is more accurate and efficient than FDM for this type of problem.
Analytical Solutions of simultaneous Linear Differential Equations in Chemica...IJMERJOURNAL
ABSTRACT: Analytical method for solving homogeneous linear differential equations in chemical kinetics and pharmacokinetics using homotopy perturbation method has been proposed. The mathematical model that depicts the pharmacokinetics is solved. Herein, we report the closed form of an analytical expression for concentrations species for all values of kinetic parameters. These results are compared with numerical results and are found to be in satisfactory agreement. The obtained results are valid for the whole solution domain.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 11: Goodness-of-Fit and Contingency Tables
11.2: Contingency Tables
On Semi-Generalized Recurrent LP-Sasakian Manifoldsinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This document provides an overview of nonparametric statistical methods for analyzing ranked data. It discusses the Wilcoxon rank-sum test and sign test, which are nonparametric alternatives to the t-test that do not assume a normal distribution. The document explains how to rank data values and handle ties. It also provides examples of using the sign test to compare a sample mean to a hypothesized value and interpreting the results.
This document presents a method for calculating a cophenetic correlation coefficient for cluster analysis performed using the modified Tocher's method. The authors extend an existing algorithm to compute a cophenetic matrix based on average distances within and between clusters formed by the modified Tocher's method. They apply their method to cluster analyses of 17 garlic cultivars based on morphological characters using Mahalanobis and Euclidean distances. They compare the cophenetic correlation coefficients obtained from the modified Tocher's method to those from hierarchical clustering methods. The results demonstrate that the proposed method reliably synthesizes the original distances into cophenetic distances and obtains cophenetic correlation coefficients consistent with previous work.
Recent research in finding the optimal path by ant colony optimizationjournalBEEI
The computation of the optimal path is one of the critical problems in graph theory. It has been utilized in various practical ranges of real world applications including image processing, file carving and classification problem. Numerous techniques have been proposed in finding optimal path solutions including using ant colony optimization (ACO). This is a nature-inspired metaheuristic algorithm, which is inspired by the foraging behavior of ants in nature. Thus, this paper study the improvement made by many researchers on ACO in finding optimal path solution. Finally, this paper also identifies the recent trends and explores potential future research directions in file carving.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document discusses a one-way analysis of variance (ANOVA) used to compare the effects of different oil types (A, B, C) on car mileage. It tests the null hypothesis that the mean mileages are equal against the alternative that at least two means differ. The ANOVA calculates sums of squares and F statistics to determine if there are significant differences between the treatment means, rejecting the null hypothesis if F exceeds the critical value. If differences exist, pairwise comparisons estimate the size of differences between each pair of means using confidence intervals.
Multiple Linear Regression Model with Two Parameter Doubly Truncated New Symm...theijes
This document presents a multiple linear regression model with errors that follow a two-parameter doubly truncated new symmetric distribution. The model extends traditional linear regression by allowing for non-Gaussian distributed errors that are finite and bounded. Properties of the doubly truncated new symmetric distribution are derived, including its probability density function and characteristic function. Maximum likelihood and ordinary least squares methods are used to estimate the model parameters. A simulation study compares the proposed model to existing models that assume Gaussian or new symmetric distributed errors.
Comparison of Several Numerical Algorithms with the use of Predictor and Corr...ijtsrd
The document discusses and compares several numerical methods for solving ordinary differential equations (ODEs), including Taylor series, Runge-Kutta, Euler's method, and predictor-corrector methods. It introduces Adams-Bashforth and Milne's predictor-corrector algorithms, which use multi-step methods to iteratively predict and correct solutions. The document also covers the basic Euler's method and improved Euler's method for solving ODEs numerically through discretization.
Hopf-Bifurcation Ina Two Dimensional Nonlinear Differential EquationIJMER
This document discusses Hopf bifurcation in a two-dimensional nonlinear differential equation. It contains the following key points:
1. The paper investigates the stability of Hopf bifurcation in a two-dimensional nonlinear differential equation, finding both supercritical and subcritical Hopf bifurcation depending on parameter values.
2. The center manifold theorem and normal forms are used to study the behavior of limit cycles created or destroyed through Hopf bifurcations.
3. Hopf bifurcation refers to the creation or destruction of a periodic solution emanating from an equilibrium point as a parameter crosses a critical value. It is important for studying oscillatory behavior in nonlinear systems.
This paper considers the control problem of a class of uncertain switched systems defined on polyhedral sets known as piecewise linear systems where, instead of the conventional Caratheodory solutions, Filippov solutions are studied. In other words, in contrast to the previous studies, solutions with infinite switching in finite time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, established upon previous studies, a set of linear matrix inequalities are brought forward which determines the asymptotic stability of piecewise linear systems with Filippov solutions. Subsequently, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed H1 performance are presented. Furthermore, these results has been generalized to the case of piecewise affine systems. Finally, a V–K iteration algorithm is proposed to deal with the aforementioned bilinear matrix inequalities. The validity of the proposed method is verified through the analysis of two simulation examples.
This document discusses moments, skewness, kurtosis, and several statistical distributions including binomial, Poisson, hypergeometric, and chi-square distributions. It defines key terms such as moment ratios, central moments, theorems, skewness, kurtosis, and correlation. Properties and applications of the binomial, Poisson, and hypergeometric distributions are provided. Finally, the document discusses the chi-square test for goodness of fit and independence.
This document provides an introduction and overview to Unit 13 of the course MST209 Mathematical methods and models. Unit 13 focuses on modelling systems using non-linear differential equations. It discusses two main examples - modeling the interaction between predator and prey populations using the Lotka-Volterra equations, and modeling the motion of a pendulum using differential equations. The unit emphasizes qualitative analysis and interpretation of solutions rather than explicit solutions. It introduces concepts like equilibrium solutions and linearizing near equilibria to understand behavior. Sections 1 and 2 develop these ideas for the Lotka-Volterra population model, while Section 3 applies similar techniques to the pendulum motion model.
Eigenvalues for HIV-1 dynamic model with two delaysIOSR Journals
This document presents a new approach to solve the characteristic equation of an HIV-1 infection dynamical system with two delays. The authors develop a series expansion to approximate the eigenvalues (roots) of the nonlinear characteristic equation. They derive the characteristic equation for the linearized HIV-1 model and nondimensionalize the equation. This allows them to express the eigenvalues as a perturbation of the logarithm of a parameter and derive an equation for the perturbation term. The goal is to make the truncated series more computationally efficient for evaluating the eigenvalues.
https://utilitasmathematica.com/index.php/Index
Our Journal has recently transitioned to becoming a fully open-access journal. This transition marks a significant shift in the landscape of academic publishing, aiming to provide numerous benefits to both authors and readers. Open access has the potential to democratize knowledge, enhance research impact, and foster greater collaboration within the academic community.
Utilitas Mathematica Journal is a broad scope journal that publishes original research and review articles on all aspects of both pure and applied mathematics.The journal publishes original research in all areas of pure and applied mathematics, statistics.
Utilitas Mathematica Journal. It's our journal publishes original research in all areas of pure and applied mathematics.Number Theory,Operations Research,Mathematical Biology,and it's the Utilitas Mathematica Journal commits to strengthening our professional .
https://utilitasmathematica.com/index
Our journal has to a fully open-access format is a significant step toward advancing the principles of open science and equitable access to knowledge. However, this transition also brings challenges, such as ensuring sustainable funding models and maintaining rigorous peer-review standards.
Overview and Implementation of Principal Component Analysis Taweh Beysolow II
This document discusses principal component analysis (PCA) and its implementation on Fisher's iris data set. PCA transforms the data to a new coordinate system where the greatest variance by each component is achieved. It was found that the first two principal components explained roughly 96% of the variance in the iris data. PCA was performed by calculating the covariance matrix and performing eigendecomposition to obtain the principal components in order of greatest variance. Projecting the iris data onto the new feature space based on the first two components revealed clusters corresponding to the three iris species.
This document provides information about the chi-square test, including:
- The chi-square test determines if there is a significant difference between expected and observed frequencies. It tests if differences are due to chance or are real differences.
- Examples of chi-square tests given include Pearson's chi-square test, Yates's correction, and tests for variance, independence, and homogeneity using contingency tables.
- Requirements for the chi-square test include quantitative data, categories, independent observations, adequate sample size, simple random sampling, and frequency data. All observations must be used.
A Class of Continuous Implicit Seventh-eight method for solving y’ = f(x, y) ...AI Publications
In this article, we develop a continuous implicit seventh-eight method using interpolation and collocation of the approximate solution for the solution of y’ = f(x, y) with a constant step-size. The method uses power series as the approximate solution in the derivation of the method. The independent solution was then derived by adopting block integrator. The properties of the method was investigated and found to be zero stable, consistent and convergent. The integrator was tested on numerical examples ranging from linear problem, Prothero-Robinson Oscillatory, Growth Model and Sir Model. The results show that the computed solution is closer to the exact solution and also, the absolutes errors perform better than the existing methods.
This document discusses analysis of variance (ANOVA), which is a statistical technique used to compare three or more population means. It begins by introducing the assumptions of ANOVA, including that populations are normally distributed and have equal variances. It then explains how ANOVA decomposes total variation into between-sample and within-sample variations. The ratio of between-sample to within-sample variation, known as the F-ratio, is used to test if population means are equal. One-way and two-way classifications of ANOVA are described.
A Stochastic Iteration Method for A Class of Monotone Variational Inequalitie...CSCJournals
We examined a general method for obtaining a solution to a class of monotone variational inequalities in Hilbert space. Let H be a real Hilbert space, and Let T : H -> H be a continuous linear monotone operator and K be a non empty closed convex subset of H. From an initial arbitrary point x0 ∈ K. We proposed and obtained iterative method that converges in norm to a solution of the class of monotone variational inequalities. A stochastic scheme {xn} is defined as follows: x(n+1) = xn - anF* (xn), n≥0, F*(xn), n ≥ 0 is a strong stochastic approximation of Txn - b, for all b (possible zero) ∈ H and an ∈ (0,1).
A Study of Some Tests of Uniformity and Their PerformancesIOSRJM
This document discusses a study that evaluates the performance of eleven tests for uniformity. The tests include Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, Watson, Sukhatme, probability product, Kuiper, Gini, ZhangA, ZhangC tests. Through simulation, the power of these tests is assessed under various sample sizes and five alternative distributions. The results are displayed in tables and graphs. The document concludes that the performance of the tests depends on the sample size and nature of the alternative distribution.
1) The document discusses contingency tables and goodness-of-fit tests. It provides objectives, definitions, notation, requirements, and examples for conducting chi-square tests of independence and homogeneity using contingency tables.
2) One example tests whether the success of a treatment for a foot injury depends on the type of treatment administered. The chi-square test rejects independence between treatment and outcome, indicating the claim that they are independent is false.
3) A second example is given where data from 3 hospitals is to be tested to see if the number of patient infections depends on the hospital. The steps for conducting this chi-square test of homogeneity are outlined.
Variance component analysis by paravayya c pujeriParavayya Pujeri
This document discusses variance component analysis and provides examples of its applications and methodology. It begins by defining key concepts such as fixed and random factors, effects, and mixed effect models. It then explains that variance component analysis partitions total variation in a dependent variable into components associated with random effects variables. The document provides examples of estimating variance components using ANOVA and examples analyzing agricultural and interlaboratory study data. It concludes that variance component analysis helps partition variation and determine where to focus efforts to reduce variance.
Chapter 11 Chi-Square Tests and ANOVA 359 Chapter .docxbartholomeocoombs
Chapter 11: Chi-Square Tests and ANOVA
359
Chapter 11: Chi-Square and ANOVA Tests
This chapter presents material on three more hypothesis tests. One is used to determine
significant relationship between two qualitative variables, the second is used to determine
if the sample data has a particular distribution, and the last is used to determine
significant relationships between means of 3 or more samples.
Section 11.1: Chi-Square Test for Independence
Remember, qualitative data is where you collect data on individuals that are categories or
names. Then you would count how many of the individuals had particular qualities. An
example is that there is a theory that there is a relationship between breastfeeding and
autism. To determine if there is a relationship, researchers could collect the time period
that a mother breastfed her child and if that child was diagnosed with autism. Then you
would have a table containing this information. Now you want to know if each cell is
independent of each other cell. Remember, independence says that one event does not
affect another event. Here it means that having autism is independent of being breastfed.
What you really want is to see if they are not independent. In other words, does one
affect the other? If you were to do a hypothesis test, this is your alternative hypothesis
and the null hypothesis is that they are independent. There is a hypothesis test for this
and it is called the Chi-Square Test for Independence. Technically it should be called
the Chi-Square Test for Dependence, but for historical reasons it is known as the test for
independence. Just as with previous hypothesis tests, all the steps are the same except for
the assumptions and the test statistic.
Hypothesis Test for Chi-Square Test
1. State the null and alternative hypotheses and the level of significance
Ho : the two variables are independent (this means that the one variable is not
affected by the other)
HA : the two variables are dependent (this means that the one variable is affected
by the other)
Also, state your α level here.
2. State and check the assumptions for the hypothesis test
a. A random sample is taken.
b. Expected frequencies for each cell are greater than or equal to 5 (The expected
frequencies, E, will be calculated later, and this assumption means E ≥ 5 ).
3. Find the test statistic and p-value
Finding the test statistic involves several steps. First the data is collected and
counted, and then it is organized into a table (in a table each entry is called a cell).
These values are known as the observed frequencies, which the symbol for an
observed frequency is O. Each table is made up of rows and columns. Then each
row is totaled to give a row total and each column is totaled to give a column
total.
Chapter 11: Chi-Squared Tests and ANOVA
360
The null hypothesis is that the variables are independent. Using the multiplication.
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Our journal has Ensuring that the statistics profession reflects the diversity of society itself is essential. Representation of underrepresented groups, including women and minorities, not only provides role models but also broadens the pool of talent and expertise in the field. Utilitas Mathematica Journal recognizes that achieving justice, equity, diversity, and inclusion is an ongoing journey that requires continuous dedication.
This document presents a stability theorem for large solutions of the three-dimensional incompressible magnetohydrodynamic equations. The theorem proves that if one solution decays to zero and another solution is initially close, then the perturbed solution will remain close. The proof uses Sobolev spaces and interpolation inequalities. As consequences of the theorem, the stability result can be extended to cases where the domain is all of R3 or satisfies certain conditions. Further work could look at extending results on regularity and stability of fluid flows to the MHD case using different function spaces like Besov spaces.
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Stochastic Model to Find the Diagnostic Reliability of Gallbladder Ejection Fraction Using Normal Distribution
1. ISSN (e): 2250 – 3005 || Vol, 04 || Issue, 8 || August – 2014 ||
International Journal of Computational Engineering Research (IJCER)
www.ijceronline.com Open Access Journal Page 36
Stochastic Model to Find the Diagnostic Reliability of Gallbladder Ejection Fraction Using Normal Distribution
P. Senthil Kumar*, A. Dinesh Kumar** & M. Vasuki*** *Assistant Professor, Department of Mathematics, Rajah Serfoji Government College (Autonomous), Thanjavur, Tamilnadu, India. **Assistant Professor, Department of Mathematics, Dhanalakshmi Srinivasan Engineering College, Perambalur, Tamilnadu, India
***Assistant Professor, Department of Mathematics, Srinivasan College of Arts and Science, Perambalur, Tamilnadu, India.
Abstract: To assess the diagnostic reliability of gallbladder ejection fraction in patients with suspected biliary pain. For a class of nonlinear diffusion equations we use the Painleve analysis. In some cases we find that it has only the conditional Painleve property and in other cases, just the painleve property. We also obtained special solutions of Painleve analysis. In that, one of the solution (i.e) the reduction of nonlinear diffusion equation to Riccati equation was used for the gallbladder ejection fraction. Key Words: Gallbladder Ejection Fraction, Normal Distribution, Painleve Property, Riccati Equation, Cholecystokinin, Chronic Acalculous Cholecystitis. 2010 Mathematics Subject Classification: 60H99, 60G99 1. Introduction: Measurement of gallbladder emptying with either oral fatty meal or intravenous administration of octapeptide of cholecystokinin (CCK-8) is a standard procedure in the evalution of patients with varieties of gallbladder diseases. When quantitative cholescintigraphy was introduced nearly 30 years ago, 10ng/kg of CCK-8 was infused intravenously over a three minute period and an ejection fraction value of 35% or greater was considered as normal. Intravenous infusion of CCK-8 has become more popular than ingestion of a fatty meal. Quantitative cholescintigraphy is critical in the evalution of hepatobiliary diseases [5], and biliary dyskinesia. Since biliary dyskinesia is purely a functional abnormality, traditional method of correlation with other imaging test such as ultrasound does not appear appropriate, and therapeutic outcome studies become critical for assessment of accuracy of diagnostic techniques. We undertook the current study in fairly large number of patients with abdominal pain to find out the therapeutic outcome results by infusing CCK-8 for three minutes. Merit of any diagnostic test depends upon its ability to separate normal subjects from those with the underlying disease [4]. In recent years, much attention has been focused on higher order non linear partial differential equations, known as evolution equations. Such nonlinear equations often occur in the description of chemical and biological phenomena. Their analytical study has been drawing immense interest. In [1], a nonlinear partial differential equation is integrable if all its exact reductions to ordinary differential equations have the Painleve property: that is, to have no movable singularities other than poles. This approach poses an obvious operational difficulty in finding all exact reductions. The reduction of to Riccati equation was used to find the gallbladder ejection fraction. 2. Notations: - Gallbladder Ejection Fraction - Cholecystokinin - Intensity - Arbitrary Function - Resonances
2. Stochastic Model To Find The Diagnostic…
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- Shape Parameter - Scale Parameter 3. Painleve Analysis: In [1], a nonlinear partial differential equation is integrable if all its exact reductions to ordinary differential equations have the Painleve property: that is, to have no movable singularities other than poles. This approach poses an obvious operational difficulty in finding all exact reductions. This difficulty was circumvented by [12] by postulating that a partial differential equation has the Painleve property if its solutions are single - valued about a movable singular manifold where is an arbitrary function. In other words, a solution of a partial differential equation should have a Laurent - like expansion about the movable singular manifold : (1) where a is a negative integer. The number of arbitrary functions in expansion (1) should be equal to the order of the partial differential equation. Inserting expansion (1) into the targeted equation yields a recurrence formula that determines for all , except for a finite number of , called resonances. For some equations, the recurrence formulas at the resonance values may result in constraint equations for the movable singular manifold which implies that it is no longer completely arbitrary. In such cases, one can say that the equation has the Conditional Painleve Property [6]. The Painleve property is a sufficient condition for the integrability or solvability of equations. Meanwhile, various authors have applied this approach to other nonlinear partial differential equations to decide whether or not these equations are integrable. Recent investigations of [2] regarding the Painleve analysis also yield a systematic procedure for obtaining special solutions when an equation possesses only the conditional Painleve property. From [3] proposed the nonlinear diffusion equation (2) as a model for the propagation of a mutant gene with an advantageous selection of intensity . From [6] has considered the extended form of equation (2) as (3) For Painleve analysis and obtained special solutions for various cases of and . In this paper we consider (4) This is a generalization of (3) for the Painleve analysis. This equation has several interesting limiting cases which have already been studied:
(i) When and , equation (4) is reduced to the generalized Fisher equation. For , equation (4) reduces to the Fisher equation and for , (4) reduces to the Newell Whitehead equation.
(ii) If we take , then equation (4) is reduced to the generalized Burgers equation. With and, equation (4) gives the Burgers equation, which describes the far field of wave propagation in nonlinear dissipative systems [13].
(iii) When and equation (4) is reduced to the generalized Burger - Fisher equation [11].
The behavior of solutions of equation (4) at a movable singular manifold, is determined by a leading order analysis where by one makes the substitution (5) and balances the most singular or dominant terms. Substituting (5) into (4), we obtain three possible values for as follows: Case (i): : Balancing the dominant terms and , we obtain
3. Stochastic Model To Find The Diagnostic…
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(6) and Case (ii): : Balancing the dominant terms and , we obtain and For , (7) Here we have two branches for as follows: Branch (i): & Branch (ii): where and (8) Case (iii): : Balancing the dominant terms and , we obtain and (9) We have the following lemma as a result. Lemma: For all combinations of integer values of and , the leading order singularity of equation (4) is
(i) A movable pole for all combinations with is equal to or for case (i), with being equal to for case (ii), and with being equal to for case (iii).
(ii) A rational branch point for all combinations with for case (i). for case (ii) and for case (iii).
The powers of , at which the arbitrary coefficient appears in the series, that is, the resonances are determined by setting and balancing the most singular terms of equation (4) again. We obtain for case (i), using the value of given by (6), with solutions However, for case (ii), with value given in (7) and for a particular value of given by (8), we obtain for branch (i) with solutions and for branch (ii)
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with solutions For case (iii), we get with solutions (10) By using the above lemma, we consider the following cases;
(i)
(ii)
(iii)
(iv)
(v)
In which equation (4) has a movable pole as leading order singularity, and therefore, it may have a valid Laurent Expansion. Now consider the case (iv): Equation (4) with In this case, equation (4) becomes (11) Using (9) and (10), we obtain and the resonances are and . Hence, we take the Laurent expansion of the form (12) Substituting (12) into (11) and collecting coefficients of equal powers of , we have (13) Equation (13) shows that is an arbitrary function. Therefore (11) possesses the Painleve property. 4. Reduction of to Riccati Equation: Let , where (14) Substituting (14) into (11) with we obtain (15) Integrating (15) once, we get (16) Equation (16) is a Riccati Equation, which can be linearized through the transformation (17) Substituting (17) into (16), we get (18)
5. Stochastic Model To Find The Diagnostic…
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which is a second order linear differential equation. Solving (18), we obtain (19) Using (19) then (17) becomes (20) 5. Example: Total of 140 subjects (113 women, 27 men) with a mean age of 46 years were selected retrospectively from a list of 444 patients. Hepatic extraction fraction and excretion halftime were determined as described [5]. Differential hepatic bile flow into gallbladder versus small intestine was calculated by dividing the total gallbladder counts by the sum of gallbladder and small intestinal counts at 60 minutes after radiotracer injection. Gallbladder phase study was obtained separately between 61 to 90 minutes by collecting data on the same size computer matrix at one frame/minute. Octapeptide of cholecystokinin (CCK-8), 10ng/kg, was infused over three minutes through an infusion pump, infusion beginning at 65 minutes after radiotracer injection (Figure 1). Gallbladder ejection fraction (GBEF) was calculated in the standard fashion [4] & [7-10]. Figure 1: In a normal subject, the gallbladder empties with an ejection fraction of 59% Figure 2: In a normal subject, the gallbladder empties with an ejection fraction of 59% (Using Normal Distribution)
6. Stochastic Model To Find The Diagnostic…
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6. Conclusion: 3 minute infusion of 10ng/kg of CCK-8 and a cut off value of 35% as the lower limit of GBEF carries a sensitivity of 95%, specificity of 89% with an overall accuracy of 92% in the evaluation of patients with chronic acalculous choleystitis (CAC). Excellent therapeutic outcome was achieved in CAC patients with laparoscopic cholecystectomy, performed solely on the basis of low ejection fraction; gallbladder ejection fraction with three minute intravenous infusion of 10ng/kg CCK-8 carries both high sensitivity and specificity and clearly separates normal gallbladder from those patients with CAC. The test is simple and reliable. This model is fairly fitted with the non linear diffusion equation by using normal distribution. The medical report {Figure (1)} is beautifully fitted with the mathematical model {Figure (2)}; (i.e) the results coincide with the mathematical and medical report. 7. References:
[1] Ablowitz M J, Ramani A & Segur H, “A Connection between Nonlinear Evolution Equations and Ordinary Differential Equations of P-type I”, Journal of Math. Physics, 21, 715-721, 1980.
[2] Cariello F & Tabor M, “Painleve Expansions for non integrable Evolution Equations”, Physica D, 39, 77-94, 1989.
[3] Fisher R A, “The wave of Advance of Advantages Genes”, Ann. Engenics 7, 355-369, 1937.
[4] Gerbail T Krishnamurthy & Shakuntala Krishnamurthy, “Diagnostic Reliability of Gallbladder Ejection Fraction”, IJNM, 13-17, 2002.
[5] Krishnamurthy G T & Krishnamurthy Ss, “A Text Book of Hepatobiliary Diseases”, New York, Springer, 2000.
[6] Roy Choudhury S, “Painleve Analysis and Partial Integrability of a Class of Reaction Diffusion Equations”, Nonlinear Analysis, TMA 18, 445-459, 1992.
[7] Senthil Kumar P & Umamaheswari N, “Stochastic Model for the Box Cox Power Transformation and Estimation of the Ex- Gaussian Distribution of Cortisol Secretion of Breast Cancer due to Smoking People”, Antarctica Journal of Mathematics, Volume 11, 99-108, 2014.
[8] P. Senthil Kumar, A. Dinesh Kumar & M. Vasuki, “Stochastic Model to find the Gallbladder Motility in Acromegaly Using Exponential Distribution”, International Journal of Engineering Research and Applications (IJERA), Volume 4, Issue 8 (Version 2), August 2014, Page Number 29-33.
[9] P. Senthil Kumar, A. Dinesh Kumar & M. Vasuki, “Stochastic Model to Find the Gallbladder Dynamics with Gallstones Results Using Exponential Distribution”, IFRSA’s International Journal of Computing (IIJC), Volume 4, Issue 3, July 2014, Page Number 619-622.
[10] P. Senthil Kumar, A. Dinesh Kumar & M. Vasuki, “Stochastic Stochastic Model to Find the Multidrug Resistance in Human Gallbladder Carcinoma Results Using Uniform Distribution”, International Journal Emerging Engineering Research and Technology (IJEERT), Volume 2, Issue 4, July 2014, Page Number 416-421.
[11] Wang X Y, Zhu Z S & Lu Y K, “Solitary Wave Solutions of the Generalized Burgers- Huxley Equation”, J. Phys. A: Math. Gen. 23, 271-274, 1990.
[12] Weiss J, Tabor M & Carnevale G, “The Painleve Property for Partial Differential Equations”, J. Math. Phys. 24, 522-526, 1983.
[13] Whitham G B, “Linear and Nonlinear Waves”, Wiley, New York, 1974.