Distributions<br />
Probability Distributions<br />Wikipedia: A probability distribution identifies either the probability of each value of an...
Types of supported distributions<br />pdf — Probability density functions<br />cdf — Cumulative distribution functions<br ...
Supported Distributions<br />Bernoulli Distribution<br />Beta Distribution<br />Binomial Distribution<br />Birnbaum-Saunde...
Hypergeometric Distribution
Inverse Gaussian Distribution
Inverse Wishart Distribution
Johnson System
Logistic Distribution
Loglogistic Distribution
Custom Distributions
Exponential Distribution
Extreme Value
Distribution
F Distribution
Gamma Distribution
Gaussian Distribution
Gaussian Mixture Distributions
Generalized Extreme Value Distribution
Generalized Pareto Distribution</li></li></ul><li>Supported Distributions<br />Lognormal Distribution<br />Multinomial Dis...
Pareto Distribution
Pearson System
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Matlab Distributions

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Probability Distributions using Matlab

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Matlab Distributions

  1. 1. Distributions<br />
  2. 2. Probability Distributions<br />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.<br />
  3. 3. Types of supported distributions<br />pdf — Probability density functions<br />cdf — Cumulative distribution functions<br />inv — Inverse cumulative distribution functions<br />stat — Distribution statistics functions<br />fit — Distribution fitting functions<br />like — Negative log-likelihood functions<br />rnd — Random number generators<br />
  4. 4. Supported Distributions<br />Bernoulli Distribution<br />Beta Distribution<br />Binomial Distribution<br />Birnbaum-Saunders Distribution<br />Chi-Square Distribution<br />Copulas<br /><ul><li>Geometric Distribution
  5. 5. Hypergeometric Distribution
  6. 6. Inverse Gaussian Distribution
  7. 7. Inverse Wishart Distribution
  8. 8. Johnson System
  9. 9. Logistic Distribution
  10. 10. Loglogistic Distribution
  11. 11. Custom Distributions
  12. 12. Exponential Distribution
  13. 13. Extreme Value
  14. 14. Distribution
  15. 15. F Distribution
  16. 16. Gamma Distribution
  17. 17. Gaussian Distribution
  18. 18. Gaussian Mixture Distributions
  19. 19. Generalized Extreme Value Distribution
  20. 20. Generalized Pareto Distribution</li></li></ul><li>Supported Distributions<br />Lognormal Distribution<br />Multinomial Distribution<br />Multivariate Gaussian Distribution<br />Multivariate Normal Distribution<br />Multivariate t Distribution<br />Nakagami Distribution<br />Negative Binomial Distribution<br />Noncentral Chi-Square Distribution<br />Noncentral F Distribution<br />Noncentral t Distribution<br />Nonparametric Distributions<br /><ul><li>Normal Distribution
  21. 21. Pareto Distribution
  22. 22. Pearson System
  23. 23. Piecewise Distributions
  24. 24. Poisson Distribution
  25. 25. Rayleigh Distribution
  26. 26. Rician Distribution
  27. 27. Student's t Distribution
  28. 28. t Location-Scale Distribution
  29. 29. Uniform Distribution (Continuous)
  30. 30. Uniform Distribution (Discrete)
  31. 31. Weibull Distribution
  32. 32. Wishart Distribution</li></li></ul><li>Probability Density functions<br />Parametric Estimation<br />Nonparametric Estimation<br />
  33. 33. 1. Parametric estimation<br /><ul><li>p = 0.2; % Probability of success for each trial
  34. 34. n = 10; % Number of trials
  35. 35. k = 0:n; % Outcomes
  36. 36. m = binopdf(k,n,p); % Probability mass vector
  37. 37. bar(k,m) % Visualize the probability distribution
  38. 38. set(get(gca,'Children'),'FaceColor',[.8 .8 1])
  39. 39. grid on</li></li></ul><li>1. Parametric estimation<br />
  40. 40. 2. Non parametric estimation<br />A distribution of data can be described graphically with a histogram:<br /><ul><li>cars = load('carsmall','MPG','Origin');
  41. 41. MPG = cars.MPG;
  42. 42. hist(MPG)
  43. 43. set(get(gca,'Children'),'FaceColor',[.8 .8 1])</li></li></ul><li>2. Non parametric estimation<br />
  44. 44. 2. Non parametric estimation<br />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:<br /><ul><li>[f,x] = ksdensity(MPG);
  45. 45. plot(x,f);
  46. 46. title('Density estimate for MPG') ;</li></li></ul><li>2. Non parametric estimation<br />
  47. 47. Cumulative Distribution Functions<br />Parametric Estimation<br />Nonparametric Estimation<br />
  48. 48. Inverse Cumulative Distribution Functions<br />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.<br />
  49. 49. Inverse Cumulative Distribution Functions<br />The expinv function can be used to compute inverses of exponential cumulative probabilities:<br />
  50. 50. Distribution Statistics Functions<br />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.<br />
  51. 51. Distribution Statistics Functions<br />For example, the wblstat function can be used to visualize the mean of the Weibull distribution as a function of its two distribution parameters:<br /><ul><li>a = 0.5:0.1:3;
  52. 52. b = 0.5:0.1:3;
  53. 53. [A,B] = meshgrid(a,b);
  54. 54. M = wblstat(A,B);
  55. 55. surfc(A,B,M)</li></li></ul><li>Distribution Statistics Functions<br />
  56. 56. Distribution Fitting Functions<br />Fitting Supported Distributions<br />Fitting Piecewise Distributions<br />
  57. 57. Negative Log-Likelihood Functions<br />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.<br />
  58. 58. Random Number Generators<br />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.<br />
  59. 59. Visit more self help tutorials<br />Pick a tutorial of your choice and browse through it at your own pace.<br />The tutorials section is free, self-guiding and will not involve any additional support.<br />Visit us at www.dataminingtools.net<br />

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