The ppt gives an idea about basic concept of Estimation. point and interval. Properties of good estimate is also covered. Confidence interval for single means, difference between two means, proportion and difference of two proportion for different sample sizes are included along with case studies.
Multiple regression analysis is a powerful technique used for predicting the unknown value of a variable from the known value of two or more variables.
This presentation includes an introduction to statistics, introduction to sampling methods, collection of data, classification and tabulation, frequency distribution, graphs and measures of central tendency.
Multiple regression analysis is a powerful technique used for predicting the unknown value of a variable from the known value of two or more variables.
This presentation includes an introduction to statistics, introduction to sampling methods, collection of data, classification and tabulation, frequency distribution, graphs and measures of central tendency.
According to Wikipedia point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population means).
Measure of dispersion has two types Absolute measure and Graphical measure. There are other different types in there.
In this slide the discussed points are:
1. Dispersion & it's types
2. Definition
3. Use
4. Merits
5. Demerits
6. Formula & math
7. Graph and pictures
8. Real life application.
It includes various cases and practice problems related to Binomial, Poisson & Normal Distributions. Detailed information on where tp use which probability.
According to Wikipedia point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population means).
Measure of dispersion has two types Absolute measure and Graphical measure. There are other different types in there.
In this slide the discussed points are:
1. Dispersion & it's types
2. Definition
3. Use
4. Merits
5. Demerits
6. Formula & math
7. Graph and pictures
8. Real life application.
It includes various cases and practice problems related to Binomial, Poisson & Normal Distributions. Detailed information on where tp use which probability.
Basic of Statistical Inference Part-III: The Theory of Estimation from Dexlab...Dexlab Analytics
In this 3rd segment of the basic of statistical inference series, the estimation theory, its elements, methods and characteristics have been discussed.
This will help understand the basic concepts of Statistics like data types, level of measurements, central tendency, dispersion, graphs, univaraite analysis, bivariate analysis and more. Moreover, it will also help you to select appropriate summary statistics and charts for your data.
Non-parametric tests are sometimes called distribution-free tests because they are based on fewer assumptions (e.g., they do not assume that the outcome is approximately normally distributed). The cost of fewer assumptions is that non-parametric tests are generally less powerful than their parametric counterparts.
Correlation & Regression Analysis using SPSSParag Shah
Concept of Correlation, Simple Linear Regression & Multiple Linear Regression and its analysis using SPSS. How it check the validity of assumptions in Regression
SPSS does not have Z test for proportions, So, we use Chi-Square test for proportion tests. Test for single proportion and Test for proportions of two samples
Chi Square test for independence of attributes / Testing association between two categorical variables, Chi-Square test for Goodness of fit / Testing significant difference between observed and expected frequencies
Chi-Square test for independence of attributes / Chi-Square test for checking association between two categorical variables, Chi-Square test for goodness of fit
t test for single mean, t test for means of independent samples, t test for means of dependent sample ( Paired t test). Case study / Examples for hands on experience of how SPSS can be used for different hypothesis testing - t test.
Basics of Hypothesis testing for PharmacyParag Shah
This presentation will clarify all basic concepts and terms of hypothesis testing. It will also help you to decide correct Parametric & Non-Parametric test for your data
Exploratory Data Analysis for Biotechnology and Pharmaceutical SciencesParag Shah
This presentation will give perfect understanding of data, data types, level of measurements, exploratory data analysis and more importantly, when to use which type of summary statistics and graphs
This presentation will clarify all your basic concepts of Probability. It includes Random Experiment, Sample Space, Event, Complementary event, Union - Intersection and difference of events, favorable cases, probability definitions, conditional probability, Bayes theorem
This ppt includes basic concepts about data types, levels of measurements. It also explains which descriptive measure, graph and tests should be used for different types of data. A brief of Pivot tables and charts is also included.
Testing of hypothesis - large sample testParag Shah
Different type of test which are used for large sample has been included in this presentation. Steps for each test and a case study is included for concept clarity and practice.
This ppt is to guide students opting for Statistics major. It gives an idea of skills required and job prospects. It also emphasizes on the important life skills along with Statistics knowledge, analytical thinking and hands on analytical software .
Opendatabay - Open Data Marketplace.pptxOpendatabay
Opendatabay.com unlocks the power of data for everyone. Open Data Marketplace fosters a collaborative hub for data enthusiasts to explore, share, and contribute to a vast collection of datasets.
First ever open hub for data enthusiasts to collaborate and innovate. A platform to explore, share, and contribute to a vast collection of datasets. Through robust quality control and innovative technologies like blockchain verification, opendatabay ensures the authenticity and reliability of datasets, empowering users to make data-driven decisions with confidence. Leverage cutting-edge AI technologies to enhance the data exploration, analysis, and discovery experience.
From intelligent search and recommendations to automated data productisation and quotation, Opendatabay AI-driven features streamline the data workflow. Finding the data you need shouldn't be a complex. Opendatabay simplifies the data acquisition process with an intuitive interface and robust search tools. Effortlessly explore, discover, and access the data you need, allowing you to focus on extracting valuable insights. Opendatabay breaks new ground with a dedicated, AI-generated, synthetic datasets.
Leverage these privacy-preserving datasets for training and testing AI models without compromising sensitive information. Opendatabay prioritizes transparency by providing detailed metadata, provenance information, and usage guidelines for each dataset, ensuring users have a comprehensive understanding of the data they're working with. By leveraging a powerful combination of distributed ledger technology and rigorous third-party audits Opendatabay ensures the authenticity and reliability of every dataset. Security is at the core of Opendatabay. Marketplace implements stringent security measures, including encryption, access controls, and regular vulnerability assessments, to safeguard your data and protect your privacy.
Data Centers - Striving Within A Narrow Range - Research Report - MCG - May 2...pchutichetpong
M Capital Group (“MCG”) expects to see demand and the changing evolution of supply, facilitated through institutional investment rotation out of offices and into work from home (“WFH”), while the ever-expanding need for data storage as global internet usage expands, with experts predicting 5.3 billion users by 2023. These market factors will be underpinned by technological changes, such as progressing cloud services and edge sites, allowing the industry to see strong expected annual growth of 13% over the next 4 years.
Whilst competitive headwinds remain, represented through the recent second bankruptcy filing of Sungard, which blames “COVID-19 and other macroeconomic trends including delayed customer spending decisions, insourcing and reductions in IT spending, energy inflation and reduction in demand for certain services”, the industry has seen key adjustments, where MCG believes that engineering cost management and technological innovation will be paramount to success.
MCG reports that the more favorable market conditions expected over the next few years, helped by the winding down of pandemic restrictions and a hybrid working environment will be driving market momentum forward. The continuous injection of capital by alternative investment firms, as well as the growing infrastructural investment from cloud service providers and social media companies, whose revenues are expected to grow over 3.6x larger by value in 2026, will likely help propel center provision and innovation. These factors paint a promising picture for the industry players that offset rising input costs and adapt to new technologies.
According to M Capital Group: “Specifically, the long-term cost-saving opportunities available from the rise of remote managing will likely aid value growth for the industry. Through margin optimization and further availability of capital for reinvestment, strong players will maintain their competitive foothold, while weaker players exit the market to balance supply and demand.”
Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
As Europe's leading economic powerhouse and the fourth-largest hashtag#economy globally, Germany stands at the forefront of innovation and industrial might. Renowned for its precision engineering and high-tech sectors, Germany's economic structure is heavily supported by a robust service industry, accounting for approximately 68% of its GDP. This economic clout and strategic geopolitical stance position Germany as a focal point in the global cyber threat landscape.
In the face of escalating global tensions, particularly those emanating from geopolitical disputes with nations like hashtag#Russia and hashtag#China, hashtag#Germany has witnessed a significant uptick in targeted cyber operations. Our analysis indicates a marked increase in hashtag#cyberattack sophistication aimed at critical infrastructure and key industrial sectors. These attacks range from ransomware campaigns to hashtag#AdvancedPersistentThreats (hashtag#APTs), threatening national security and business integrity.
🔑 Key findings include:
🔍 Increased frequency and complexity of cyber threats.
🔍 Escalation of state-sponsored and criminally motivated cyber operations.
🔍 Active dark web exchanges of malicious tools and tactics.
Our comprehensive report delves into these challenges, using a blend of open-source and proprietary data collection techniques. By monitoring activity on critical networks and analyzing attack patterns, our team provides a detailed overview of the threats facing German entities.
This report aims to equip stakeholders across public and private sectors with the knowledge to enhance their defensive strategies, reduce exposure to cyber risks, and reinforce Germany's resilience against cyber threats.
Adjusting primitives for graph : SHORT REPORT / NOTESSubhajit Sahu
Graph algorithms, like PageRank Compressed Sparse Row (CSR) is an adjacency-list based graph representation that is
Multiply with different modes (map)
1. Performance of sequential execution based vs OpenMP based vector multiply.
2. Comparing various launch configs for CUDA based vector multiply.
Sum with different storage types (reduce)
1. Performance of vector element sum using float vs bfloat16 as the storage type.
Sum with different modes (reduce)
1. Performance of sequential execution based vs OpenMP based vector element sum.
2. Performance of memcpy vs in-place based CUDA based vector element sum.
3. Comparing various launch configs for CUDA based vector element sum (memcpy).
4. Comparing various launch configs for CUDA based vector element sum (in-place).
Sum with in-place strategies of CUDA mode (reduce)
1. Comparing various launch configs for CUDA based vector element sum (in-place).
2. Parameter and Statistics
• A measure calculated from population data is called
Parameter.
• A measure calculated from sample data is called Statistic.
Parameter Statistic
Size N n
Mean μ x̄
Standard deviation σ s
Proportion P p
Correlation coefficient ρ r
3. Statistical Inference
The method to infer about population on the basis of sample
information is known as Statistical inference.
It mainly consists of two parts:
• Estimation
• Testing of Hypothesis
4. Estimation
Estimation is a process whereby we select a random sample from
a population and use a sample statistic to estimate a population
parameter.
There are two ways for estimation:
• Point Estimation
• Interval Estimation
5. Point Estimate
Point Estimate – A sample statistic used to estimate the exact
value of a population parameter.
• A point estimate is a single value and has the advantage of
being very precise but there is no information about its
reliability.
• The probability that a single sample statistic actually equal to
the parameter value is extremely small. For this reason point
estimation is rarely used.
7. Unbiasedness
Any sample statistic is said to be an unbiased estimator for the
population parameter if on an average the value sample statistic
is equal to the parameter value.
e.g. 𝐸 𝑥 = 𝜇 i.e. sample mean is an unbiased estimator of
population mean
8. Consistency
An estimator is said to be a consistent estimator for the
parameter if the value of statistics gets closer to the value of the
parameter and the respective variance of statistics get closer to
zero as sample size increases.
e.g. 𝐸 𝑥 → 𝜇 and 𝑉 𝑥 =
𝜎2
𝑛
→ 0 as sample size n increases
9. Sufficiency
If a statistic contain almost all information regarding the
population parameter that is contained in the population then
the statistic is called sufficient estimator for the parameter.
10. Efficiency
An estimator is said to be an efficient estimator if it contains
smaller variance among all variances of all other estimators.
11. Interval Estimate
Confidence interval (interval estimate) – A range of values
defined by the confidence level within which the population
parameter is estimated to fall.
• The interval estimate is less precise, but gives more
confidence.
12. Example of Point and Interval Estimate
Government wants to know the percentage of cigarette smokers
among college students.
If we say that there was 10% are smokers, it is a point estimate.
But if we make a statement that 8% to 12% of college students
are smokers, it is interval estimate.
13. Sampling distribution
From a population of size N, number of samples of size n can be
selected and these samples give different values of a statistics.
These different values of statistic can be arranged in form of a
frequency distribution which is known as sampling distribution
of that statistics.
We can have sampling distribution of sample mean, sampling
distribution of sample proportion etc.
14. Standard Error of a statistics
The standard deviation calculated from the observations of a
sampling distribution of a statistics is called Standard Error of
that statistics.
E.g. The standard deviation calculated from the observations of
sampling distribution of x̄ is called standard error of x̄. It is
denoted by S.E.(x̄)
15. Standard Error for Mean
when population standard deviation (𝜎) is known
S.E.( 𝑥 ) =
𝜎
𝑛
for infinite population
S.E.( 𝑥 ) =
𝜎
𝑛
∗
𝑁−𝑛
𝑁−1
for finite population
16. Standard Error for Mean
when population standard deviation (𝜎) is unknown
When sample size is large ( n > 30)
S.E.( 𝑥 ) =
𝑠
𝑛
for infinite population
S.E.( 𝑥 ) =
𝑠
𝑛
∗
𝑁− 𝑛
𝑁−1
for finite population
When sample size is small ( n ≤ 30)
S.E.( 𝑥 ) =
𝑠
𝑛−1
for infinite population
S.E.( 𝑥 ) =
𝑠
𝑛−1
∗
𝑁− 𝑛
𝑁−1
for finite population
17. Standard Error for difference between two means
when population standard deviation (𝜎) is known
S.E.(𝑥1 − 𝑥2) =
𝜎1
2
𝑛1
+
𝜎2
2
𝑛2
18. Standard Error for difference between two means
when population standard deviation (𝜎) is unknown
When sample size is large ( n > 30)
S.E.(𝑥1 − 𝑥2) =
𝑠1
2
𝑛1
+
𝑠2
2
𝑛2
When sample size is small ( n ≤ 30)
S.E.(𝑥1 − 𝑥2) = 𝑠2(
1
𝑛1
+
1
𝑛2
)
Where
𝑠2 =
𝑛1∗𝑠1
2+𝑛2∗𝑠2
2
𝑛1+𝑛2−2
19. Standard Error for Proportion
S.E. (𝑝) =
𝑃𝑄
𝑛
for infinite population
S.E. (𝑝) =
𝑃𝑄
𝑛
𝑁−𝑛
𝑁−1
for finite population
When population proportion (𝑃) is unknown, then it is estimated by sample
proportion (𝑝)
20. Standard Error for difference between two proportions
Population proportions are known
S.E.(𝑝1 − 𝑝2) =
𝑃1 𝑄1
𝑛1
+
𝑃2 𝑄2
𝑛2
Population proportions are unknown
S.E.(𝑝1 − 𝑝2) = 𝑃 ∗ 𝑄 (
1
𝑛1
+
1
𝑛2
)
where
𝑃 =
𝑛1 𝑝1 + 𝑛2 𝑝2
𝑛1 + 𝑛2
21. Interval Estimation
Confidence Interval has the form:
Point estimate ± Margin of error
Where
Margin of error = Critical value of estimate * Standard Error of estimate
22. z table value
1 % 5% 10%
Two tailed test (≠ ) 2.58 1.96 1.645
One tailed test ( > or < ) 2.33 1.645 1.28
23.
24. C.I. for Population mean
(i) When Population standard deviation is known or the sample
size is large
𝑥 ± 𝑍 𝛼 × S.E.( 𝑥 )
(ii) When Population standard deviation is unknown and the
sample size is small
𝑥 ± 𝑡 𝛼,𝑛−1 × S.E.( 𝑥 )
25. Case Study 1
A government agency was charged by the legislature with estimating the
length of time it takes citizens to fill out various forms. Two hundred
randomly selected adults were timed as they filled out a particular form.
The times required had mean 12.8 minutes with standard deviation 1.7
minutes.
Construct a 90% confidence interval for the mean time taken for all adults
to fill out this form.
26. Case Study 2
A thread manufacturer tests a sample of eight lengths of a
certain type of thread made of blended materials and obtains a
mean tensile strength of 8.2 lb with standard deviation 0.06 lb.
Assuming tensile strengths are normally distributed, construct a
90% confidence interval for the mean tensile strength of this
thread.
27. C.I. for difference between two means
(i) When Population standard deviation is known or the sample
size is large
(𝑥1 − 𝑥2) ± 𝑍 𝛼 × S.E.(𝑥1 − 𝑥2)
(ii) When Population standard deviation is unknown and the
sample size is small
(𝑥1 − 𝑥2) ± 𝑡 𝛼,𝑛1+𝑛2−2 × S.E.(𝑥1 − 𝑥2)
28. Case Study 1
Records of 40 used passenger cars and 40 used pickup trucks
(none used commercially) were randomly selected to investigate
whether there was any difference in the mean time in years that
they were kept by the original owner before being sold. For cars
the mean was 5.3 years with standard deviation 2.2 years. For
pickup trucks the mean was 7.1 years with standard deviation 3.0
years. Construct the 95% confidence interval for the difference in
the means based on these data.
29. Case Study 2
A university administrator wishes to know if there is a difference in average
starting salary for graduates with master’s degrees in engineering and those
with master’s degrees in business. Fifteen recent graduates with master’s
degree in engineering and 11 with master’s degrees in business are surveyed
and the results are summarized below. Construct the 99% confidence interval
for the difference in the population means based on these data.
n Mean Std. dev
Engineering 15 68,535 1627
Business 11 63,230 2033
31. Case Study
In a random sample of 2,300 mortgages taken out in a certain
region last year, 187 were adjustable-rate mortgages. Assuming
that the sample is sufficiently large, construct a 99% confidence
interval for the proportion of all mortgages taken out in this
region last year that were adjustable-rate mortgages.
33. Case Study
A survey for anemia prevalence among women in developing
countries was conducted among African and Asian women. Out
of 2100 African women, 840 were anemia and out of 1900 Asian
women, 323 were anemia. Find a 95% confidence interval for the
difference in proportions of all African women with anemia and
all women from the Asian with anemia.