Statistics and Distributions using Matlab

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

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

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

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])

41. MPG = cars.MPG;

42. hist(MPG)

45. plot(x,f);

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.

52. b = 0.5:0.1:3;

53. [A,B] = meshgrid(a,b);

54. M = wblstat(A,B);

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.

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