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Matlab Distributions

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Probability Distributions using Matlab

Probability Distributions using Matlab

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  • 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:
    • 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 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