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# Matlab Distributions

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Probability Distributions using Matlab

Probability Distributions using Matlab

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Statistics
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### Transcript

• 1. Distributions
• 2. Probability Distributions
Wikipedia: A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous). The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.
• 3. Types of supported distributions
pdf — Probability density functions
cdf — Cumulative distribution functions
inv — Inverse cumulative distribution functions
stat — Distribution statistics functions
fit — Distribution fitting functions
like — Negative log-likelihood functions
rnd — Random number generators
• 4. Supported Distributions
Bernoulli Distribution
Beta Distribution
Binomial Distribution
Birnbaum-Saunders Distribution
Chi-Square Distribution
Copulas
• Geometric Distribution
• 5. Hypergeometric Distribution
• 6. Inverse Gaussian Distribution
• 7. Inverse Wishart Distribution
• 8. Johnson System
• 9. Logistic Distribution
• 10. Loglogistic Distribution
• 11. Custom Distributions
• 12. Exponential Distribution
• 13. Extreme Value
• 14. Distribution
• 15. F Distribution
• 16. Gamma Distribution
• 17. Gaussian Distribution
• 18. Gaussian Mixture Distributions
• 19. Generalized Extreme Value Distribution
• 20. Generalized Pareto Distribution
• Supported Distributions
Lognormal Distribution
Multinomial Distribution
Multivariate Gaussian Distribution
Multivariate Normal Distribution
Multivariate t Distribution
Nakagami Distribution
Negative Binomial Distribution
Noncentral Chi-Square Distribution
Noncentral F Distribution
Noncentral t Distribution
Nonparametric Distributions
• Normal Distribution
• 21. Pareto Distribution
• 22. Pearson System
• 23. Piecewise Distributions
• 24. Poisson Distribution
• 25. Rayleigh Distribution
• 26. Rician Distribution
• 27. Student's t Distribution
• 28. t Location-Scale Distribution
• 29. Uniform Distribution (Continuous)
• 30. Uniform Distribution (Discrete)
• 31. Weibull Distribution
• 32. Wishart Distribution
• Probability Density functions
Parametric Estimation
Nonparametric Estimation
• 33. 1. Parametric estimation
• p = 0.2; % Probability of success for each trial
• 34. n = 10; % Number of trials
• 35. k = 0:n; % Outcomes
• 36. m = binopdf(k,n,p); % Probability mass vector
• 37. bar(k,m) % Visualize the probability distribution
• 38. set(get(gca,'Children'),'FaceColor',[.8 .8 1])
• 39. grid on
• 1. Parametric estimation
• 40. 2. Non parametric estimation
A distribution of data can be described graphically with a histogram:
• 41. MPG = cars.MPG;
• 42. hist(MPG)
• 43. set(get(gca,'Children'),'FaceColor',[.8 .8 1])
• 2. Non parametric estimation
• 44. 2. Non parametric estimation
You can also describe a data distribution by estimating its density. The ksdensity function does this using a kernel smoothing method. A nonparametric density estimate of the data above, using the default kernel and bandwidth, is given by:
• [f,x] = ksdensity(MPG);
• 45. plot(x,f);
• 46. title('Density estimate for MPG') ;
• 2. Non parametric estimation
• 47. Cumulative Distribution Functions
Parametric Estimation
Nonparametric Estimation
• 48. Inverse Cumulative Distribution Functions
Each function in this family represents a parametric family of distributions. Input arguments are arrays of cumulative probabilities between 0 and 1 followed by a list of parameter values specifying a particular member of the distribution family.
• 49. Inverse Cumulative Distribution Functions
The expinv function can be used to compute inverses of exponential cumulative probabilities:
• 50. Distribution Statistics Functions
Each function in this family represents a parametric family of distributions. Input arguments are lists of parameter values specifying a particular member of the distribution family. Functions return the mean and variance of the distribution, as a function of the parameters.
• 51. Distribution Statistics Functions
For example, the wblstat function can be used to visualize the mean of the Weibull distribution as a function of its two distribution parameters:
• Distribution Statistics Functions
• 56. Distribution Fitting Functions
Fitting Supported Distributions
Fitting Piecewise Distributions
• 57. Negative Log-Likelihood Functions
Each function in this family represents a parametric family of distributions. Input arguments are lists of parameter values specifying a particular member of the distribution family followed by an array of data. Functions return the negative log-likelihood of the parameters, given the data.
• 58. Random Number Generators
Each RNG represents a parametric family of distributions. Input arguments are lists of parameter values specifying a particular member of the distribution family followed by the dimensions of an array. RNGs return random numbers from the specified distribution in an array of the specified dimensions.
• 59. Visit more self help tutorials
Pick a tutorial of your choice and browse through it at your own pace.
The tutorials section is free, self-guiding and will not involve any additional support.
Visit us at www.dataminingtools.net