Matlab: Statistics and Distributions
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This document discusses probability distributions and provides an overview of the types of distributions and functions supported in the Statistics and Machine Learning Toolbox. It describes probability distributions as identifying the probability of values a random variable can take. It lists several common distributions like the binomial, normal, and lognormal distributions. It then summarizes the different types of functions available for parametric estimation, nonparametric estimation, inverse cumulative distribution functions, distribution statistics, distribution fitting, negative log-likelihood, and random number generation.
Matlab: Statistics and Distributions
- 2. Probability DistributionsWikipedia: 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 distributionspdf — Probability density functionscdf — Cumulative distribution functionsinv — Inverse cumulative distribution functionsstat — Distribution statistics functionsfit — Distribution fitting functionslike — Negative log-likelihood functionsrnd — Random number generators
- 4. Supported DistributionsBernoulli DistributionBeta DistributionBinomial DistributionBirnbaum-Saunders DistributionChi-Square DistributionCopulasGeometric Distribution
- 13. Extreme Value
- 14. Distribution
- 15. F Distribution
- 19. Generalized Extreme Value Distribution
- 20. Generalized Pareto DistributionSupported DistributionsLognormal DistributionMultinomial DistributionMultivariate Gaussian DistributionMultivariate Normal DistributionMultivariate t DistributionNakagami DistributionNegative Binomial DistributionNoncentral Chi-Square DistributionNoncentral F DistributionNoncentral t DistributionNonparametric DistributionsNormal Distribution
- 22. Pearson System
- 32. Wishart DistributionProbability Density functionsParametric EstimationNonparametric Estimation
- 33. 1. Parametric estimationp = 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
- 39. grid on1. Parametric estimation
- 40. 2. Non parametric estimationA distribution of data can be described graphically with a histogram:cars = load('carsmall','MPG','Origin');
- 41. MPG = cars.MPG;
- 42. hist(MPG)
- 43. set(get(gca,'Children'),'FaceColor',[.8 .8 1])2. Non parametric estimation
- 44. 2. Non parametric estimationYou 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 FunctionsParametric EstimationNonparametric Estimation
- 48. Inverse Cumulative Distribution FunctionsEach 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 FunctionsThe expinv function can be used to compute inverses of exponential cumulative probabilities:
- 50. Distribution Statistics FunctionsEach 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 FunctionsFor example, the wblstat function can be used to visualize the mean of the Weibull distribution as a function of its two distribution parameters:a = 0.5:0.1:3;
- 52. b = 0.5:0.1:3;
- 54. M = wblstat(A,B);
- 56. Distribution Fitting FunctionsFitting Supported DistributionsFitting Piecewise Distributions
- 57. Negative Log-Likelihood FunctionsEach 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 GeneratorsEach 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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