Probability Distribution Ontology

ProbOnto, is an ontology-based knowledge base of probability distributions, featuring more than eighty uni- and multivariate distributions with their defining functions, characteristics, relationships and reparameterisation formulas.

  Amoroso 1
  Arcsine 1
  Arcsine 2
  Asymmetric Laplace 1
  Benford 1
  Bernoulli 1
  Bernoulli 2
  Beta 1
  Beta Pascal
  Beta-binomial 1
  Binomial 1
  Binomial 2
  Birnbaum-Saunders 1
  Borel 1
  Breit-Wigner
  Burr Type XII
  CDF of Arcsine 1
  CDF of Arcsine 2
  CDF of Asymmetric Laplace 1
  CDF of Benford 1
  CDF of Bernoulli 1
  CDF of Beta 1
  CDF of Beta Negative Binomial1
  CDF of Beta-binomial 1
  CDF of Binomial 1
  CDF of Binomial 2
  CDF of Birnbaum-Saunders 1
  CDF of Borel 1
  CDF of Burr 1
  CDF of Categorical Nonordered 1
  CDF of Categorical Ordered 1
  CDF of Cauchy 1
  CDF of Chi 1
  CDF of Chi-squared 1
  CDF of Conway-Maxwell-Poisson 1
  CDF of Dagum 1
  CDF of Double Poisson 1
  CDF of Epanechnikov 1
  CDF of Erlang 1
  CDF of Exponential 1
  CDF of Exponential 2
  CDF of Exponentially modified Gaussian 1
  CDF of F 1
  CDF of Folded Normal 1
  CDF of Frechet 1
  CDF of Frechet 2
  CDF of Gamma 1
  CDF of Gamma 2
  CDF of Generalized Gamma 1
  CDF of Generalized Gamma 2
  CDF of Generalized Negative Binomial 1
  CDF of Generalized Poisson 1
  CDF of Generalized Poisson 3
  CDF of GeneralizedPoisson2
  CDF of Geometric 1
  CDF of Gompertz 1
  CDF of Gumbel 1
  CDF of Half Cauchy 1
  CDF of Half-normal 1
  CDF of Half-normal 2
  CDF of Hyperbolic secant 1
  CDF of Hypergeometric 1
  CDF of Inverse Chi-Square
  CDF of Inverse Gaussian 1
  CDF of Inverse-Gamma 1
  CDF of Johnson SB 1
  CDF of Johnson SL 1
  CDF of Johnson SN 1
  CDF of Johnson SU 1
  CDF of Kumaraswamy 1
  CDF of Laplace 1
  CDF of Laplace 2
  CDF of Levy 1
  CDF of Log-Logistic 1
  CDF of Log-Logistic 2
  CDF of Log-Normal 1
  CDF of Log-Normal 2
  CDF of Log-Normal 3
  CDF of Log-Normal 4
  CDF of Log-Normal 5
  CDF of Log-Normal 6
  CDF of Log-Normal 7
  CDF of Log-Uniform 1
  CDF of Logistic 1
  CDF of Logistic 2
  CDF of Logit Normal 1
  CDF of Lomax 1
  CDF of Makeham 1
  CDF of Maxwell Boltzmann 1
  CDF of Multivariate Normal 1
  CDF of Multivariate Normal 2
  CDF of Multivariate Student T 1
  CDF of Muth 1
  CDF of Nakagami 1
  CDF of Negative Binomial 1
  CDF of Negative Binomial 2
  CDF of Negative Binomial 4
  CDF of Negative Binomial 5
  CDF of Noncentral Beta 1
  CDF of Noncentral F 1
  CDF of Noncentral chi-squared 1
  CDF of Normal 1
  CDF of Normal 2
  CDF of Normal 3
  CDF of Pareto Type I
  CDF of Pareto Type II
  CDF of Poisson 1
  CDF of Poisson 2
  CDF of Power 1
  CDF of Power-Normal 1
  CDF of Rayleigh 1
  CDF of Scaled Inverse Chi-Square
  CDF of Sinh-Arcsinh 2
  CDF of Skew Normal
  CDF of Standard Cauchy 1
  CDF of Standard Logistic 1
  CDF of Standard Normal 1
  CDF of Standard Power 1
  CDF of Standard Triangular 1
  CDF of Standard Two-Sided Power 1
  CDF of Standard Uniform 1
  CDF of Student's t-distribution 1
  CDF of Trapezoidal 1
  CDF of Triangular 1
  CDF of Truncated Normal 1
  CDF of Two-Sided Power 1
  CDF of Uniform 1
  CDF of Uniform Discrete 1
  CDF of Uniform Discrete 2
  CDF of Von Mises 1
  CDF of Weibull 1
  CDF of Weibull 2
  CDF of Weibull Discrete 1
  CDF of Wigner Semicircle 1
  CDF of YuleSimon1
  CDF of Zero-Inflated Generalized Poisson 1
  CDF of Zero-Inflated Negative Binomial 1
  CDF of Zero-inflated Poisson 1
  CDF of Zeta 1
  CDF of Zipf 1
  Categorical Nonordered 1
  Categorical Ordered 1
  Chi 1
  Chi-square
  Cholesky parameterization
  Conway-Maxwell-Poisson 1
  Dagum 1
  Dirichlet
  Double Exponential 2
  Double Poisson 1
  Epanechnikov 1
  Erlang 1
  ExGaussian
  Exponential 1
  Exponential 2
  F 1
  Fisk
  Fisk
  Folded Normal 1
  Frechet 1
  Galton
  Galton
  Galton
  Galton
  Gamma 1
  Gamma 2
  Gaussian- inverse-gamma
  Generalized Gamma 1
  Generalized Gamma 2
  Generalized Gamma 3
  Generalized Negative Binomial 1
  Generalized Poisson 1
  Generalized Poisson 3
  GeneralizedPoisson2
  Geometric 1
  Gompertz 1
  Gumbel 1
  HF of Arcsine 1
  HF of Benford 1
  HF of Beta 1
  HF of Burr 1
  HF of Erlang 1
  HF of Exponential 1
  HF of Exponential 2
  HF of Geometric 1
  HF of Gompertz 1
  HF of Kumaraswamy 1
  HF of Log-Logistic 2
  HF of Makeham 1
  HF of Muth 1
  HF of Power 1
  HF of Standard Cauchy 1
  HF of Standard Normal 1
  HF of Standard Power 1
  HF of Standard Triangular 1
  HF of Two-Sided Power 1
  HF of Uniform Discrete 2
  HF of Weibull 1
  HF of Weibull 2
  HF of Weibull Discrete 1
  Half Cauchy 1
  Half-normal 1
  Half-normal 2
  Hyperbolic secant 1
  Hypergeometric 1
  Inverse Binomial 1
  Inverse Weibull
  Inverse-Gamma 1
  Inverse-Wishart 1
  Inverted-chi-square
  Johnson SB 1
  Johnson SL 1
  Johnson SN 1
  Johnson SU 1
  LKJ Correlation 1
  LKJ Correlation 2
  Laplace 1
  Level end of Trapezoidal-1
  Level start of Trapezoidal-1
  Levy 1
  Log-Normal 2
  Log-Normal 3
  Log-Uniform 1
  Logistic 1
  Logistic 2
  Logit Normal 1
  Lomax 1
  Lower bound of Trapezoidal-1
  Lower bound of Two-Sided-Power-1
  Makeham 1
  Maxwell Boltzmann 1
  Minimax distribution
  Mixture Distribution 1
  Multinomial 1
  Multivariate Gaussian 2
  Multivariate Gaussian Process Distribution 1
  Multivariate Normal 1
  Multivariate Normal 3
  Multivariate Student T 1
  Multivariate Student T 2
  Muth 1
  NA of Makeham-1
  NA of Makeham-1
  NA of Makeham-1
  Nakagami 1
  Negative Binomial 1
  Negative Binomial 2
  Negative Binomial 3
  Negative Binomial 4
  Negative Binomial 5
  Negative Binomial 6
  Noncentral Beta 1
  Noncentral F 1
  Noncentral chi-squared 1
  NoncentralT
  Normal
  Normal
  Normal 2
  Ordered Logistic 1
  PDF of Amoroso 1
  PDF of Arcsine 1
  PDF of Arcsine 2
  PDF of Asymmetric Laplace 1
  PDF of Beta 1
  PDF of Birnbaum-Saunders 1
  PDF of Burr 1
  PDF of Cauchy 1
  PDF of Chi 1
  PDF of Chi-squared 1
  PDF of Dagum 1
  PDF of Dirichlet 1
  PDF of Epanechnikov 1
  PDF of Erlang 1
  PDF of Exponential 1
  PDF of Exponential 2
  PDF of Exponentially modified Gaussian 1
  PDF of F 1
  PDF of Folded Normal 1
  PDF of Frechet 1
  PDF of Frechet 2
  PDF of Gamma 1
  PDF of Gamma 2
  PDF of Generalized Gamma 1
  PDF of Generalized Gamma 2
  PDF of Generalized Gamma 3
  PDF of Gompertz 1
  PDF of Gumbel 1
  PDF of Half Cauchy 1
  PDF of Half-normal 1
  PDF of Half-normal 2
  PDF of Hyperbolic secant 1
  PDF of Inverse Chi-Square
  PDF of Inverse Gaussian 1
  PDF of Inverse-Gamma 1
  PDF of Inverse-Wishart 1
  PDF of Johnson SB 1
  PDF of Johnson SL 1
  PDF of Johnson SN 1
  PDF of Johnson SU 1
  PDF of Kumaraswamy 1
  PDF of LKJ Correlation 1
  PDF of LKJ Correlation 2
  PDF of Laplace 1
  PDF of Laplace 2
  PDF of Levy 1
  PDF of Log-Logistic 1
  PDF of Log-Logistic 2
  PDF of Log-Normal 1
  PDF of Log-Normal 2
  PDF of Log-Normal 3
  PDF of Log-Normal 4
  PDF of Log-Normal 5
  PDF of Log-Normal 6
  PDF of Log-Normal 7
  PDF of Log-Uniform 1
  PDF of Logistic 1
  PDF of Logistic 2
  PDF of Logit Normal 1
  PDF of Lomax 1
  PDF of Makeham 1
  PDF of Maxwell Boltzmann 1
  PDF of Mixture Distribution 1
  PDF of Multivariate Gaussian Process Distribution 1
  PDF of Multivariate Gaussian Process Distribution 2
  PDF of Multivariate Normal 1
  PDF of Multivariate Normal 2
  PDF of Multivariate Normal 3
  PDF of Multivariate Student T 1
  PDF of Multivariate Student T 2
  PDF of Muth 1
  PDF of Nakagami 1
  PDF of Noncentral Beta 1
  PDF of Noncentral F 1
  PDF of Noncentral chi-squared 1
  PDF of NoncentralT
  PDF of Normal 1
  PDF of Normal 2
  PDF of Normal 3
  PDF of Normal-inverse-gamma 1
  PDF of Pareto Type I
  PDF of Pareto Type II
  PDF of Power 1
  PDF of Power-Normal 1
  PDF of Rayleigh 1
  PDF of Rice 1
  PDF of Scaled Inverse Chi-Square
  PDF of Sinh-Arcsinh 1
  PDF of Sinh-Arcsinh 2
  PDF of Skew Normal
  PDF of Standard Cauchy 1
  PDF of Standard Logistic 1
  PDF of Standard Normal 1
  PDF of Standard Power 1
  PDF of Standard Triangular 1
  PDF of Standard Two-Sided Power 1
  PDF of Standard Uniform 1
  PDF of Student's t-distribution 1
  PDF of Student's t-distribution 2
  PDF of Student's t-distribution 3
  PDF of Trapezoidal 1
  PDF of Triangular 1
  PDF of Truncated Normal 1
  PDF of Two-Sided Power 1
  PDF of Uniform 1
  PDF of Von Mises 1
  PDF of Weibull 1
  PDF of Weibull 2
  PDF of Wiener Diffusion Model 1
  PDF of Wigner Semicircle 1
  PDF of Wishart 1
  PDF of Wishart 2
  PMF of Benford 1
  PMF of Bernoulli 1
  PMF of Bernoulli 2
  PMF of Beta Negative Binomial1
  PMF of Beta-binomial 1
  PMF of Binomial 1
  PMF of Binomial 2
  PMF of Borel 1
  PMF of Categorical Nonordered 1
  PMF of Categorical Ordered 1
  PMF of Conway-Maxwell-Poisson 1
  PMF of Double Poisson 1
  PMF of Generalized Negative Binomial 1
  PMF of Generalized Poisson 1
  PMF of Generalized Poisson 3
  PMF of GeneralizedPoisson2
  PMF of Geometric 1
  PMF of Hypergeometric 1
  PMF of Inverse Binomial 1
  PMF of Mixture Distribution 1
  PMF of Multinomial 1
  PMF of Negative Binomial 1
  PMF of Negative Binomial 2
  PMF of Negative Binomial 3
  PMF of Negative Binomial 4
  PMF of Negative Binomial 5
  PMF of Negative Binomial 6
  PMF of Ordered Logistic 1
  PMF of Poisson 1
  PMF of Poisson 2
  PMF of Uniform Discrete 1
  PMF of Uniform Discrete 2
  PMF of Weibull Discrete 1
  PMF of YuleSimon1
  PMF of Zero-Inflated Generalized Poisson 1
  PMF of Zero-Inflated Negative Binomial 1
  PMF of Zero-inflated Poisson 1
  PMF of Zeta 1
  PMF of Zipf 1
  Pareto Type I
  Pareto Type II
  Poisson 1
  Poisson 2
  Poisson intensity of Conway-Maxwell-Poisson-1
  Poisson intensity of Double-Poisson-1
  Poisson intensity of Generalized-Poisson-1
  Poisson intensity of Negative-Binomial-2
  Poisson intensity of Poisson-1
  Poisson intensity of Zero-inflated-Poisson-1
  Power 1
  Power-Normal 1
  Rayleigh 1
  Rectangular Continuous
  Rectangular Discrete 1
  Rician
  SF of Arcsine 1
  SF of Benford 1
  SF of Beta 1
  SF of Burr 1
  SF of Erlang 1
  SF of Exponential 1
  SF of Exponential 2
  SF of Gamma 1
  SF of Geometric 1
  SF of Gompertz 1
  SF of Half Cauchy 1
  SF of Kumaraswamy 1
  SF of Log-Logistic 2
  SF of Makeham 1
  SF of Muth 1
  SF of Power 1
  SF of Standard Cauchy 1
  SF of Standard Normal 1
  SF of Standard Power 1
  SF of Standard Triangular 1
  SF of Standard Uniform 1
  SF of Two-Sided Power 1
  SF of Uniform Discrete 2
  SF of Weibull 1
  SF of Weibull 2
  SF of Weibull Discrete 1
  SHASH
  STSP
  Scaled Inverse Chi-Square
  Sinh-Arcsinh 2
  Skew Normal
  Standard Cauchy 1
  Standard Logistic 1
  Standard Normal 1
  Standard Power 1
  Standard Triangular 1
  Standard Uniform 1
  Student's t-distribution 1
  Student's t-distribution 2
  Trapezoidal 1
  Triangular 1
  Truncated Normal 1
  Two-Sided Power 1
  Uniform Discrete 2
  Upper bound of Trapezoidal-1
  Von Mises 1
  Wald
  Weibull 1
  Weibull 2
  Weibull Discrete 1
  Wiener Diffusion Model 1
  Wigner Semicircle 1
  Wishart 1
  Wishart 2
  YuleSimon1
  Zero-Inflated Generalized Poisson 1
  Zero-Inflated Negative Binomial 1
  Zero-inflated Poisson 1
  Zeta 1
  Zipf 1
  boundary separation of Wiener-Diffusion-Model-1
  category probabilities of Categorical-Nonordered-1
  category probabilities of Categorical-Ordered-1
  coefficient of variation of Log-Normal-4
  concentration of Dirichlet-1
  concentration of Von-Mises-1
  covariance matrix of Multivariate-Normal-1
  covariance matrix of Multivariate-Student-T-1
  degree of freedom of F-1
  degree of freedom of F-1
  degrees of freedom of Chi-1
  degrees of freedom of Chi-squared-1
  degrees of freedom of Inverse-Chi-Square
  degrees of freedom of Inverse-Wishart-1
  degrees of freedom of Multivariate-Student-T-1
  degrees of freedom of Multivariate-Student-T-2
  degrees of freedom of Noncentral-F-1
  degrees of freedom of Noncentral-F-1
  degrees of freedom of Noncentral-chi-squared-1
  degrees of freedom of NoncentralT
  degrees of freedom of Scaled-Inverse-Chi-Square
  degrees of freedom of Student-s-t-distribution-1
  degrees of freedom of Student-s-t-distribution-2
  degrees of freedom of Student-s-t-distribution-3
  degrees of freedom of Wishart-1
  degrees of freedom of Wishart-2
  dispersion of Double-Poisson-1
  dispersion of Generalized-Poisson-1
  dispersion of Generalized-Poisson-3
  dispersion of GeneralizedPoisson2
  dispersion of Zero-Inflated-Generalized-Poisson-1
  drift rate of Wiener-Diffusion-Model-1
  event probabilities of Multinomial-1
  index parameter of Inverse-Binomial-1
  index parameter of Negative-Binomial-3
  index parameter of Negative-Binomial-6
  initial bias of Wiener-Diffusion-Model-1
  inverse scale matrix of Wishart-2
  inverse scale of Half-normal-1
  inverse scale of Logistic-2
  inverse scale of Negative-Binomial-5
  kurtosis of Sinh-Arcsinh-2
  lambda of Normal-inverse-gamma-1
  lambda of Weibull-2
  left beta parameter of Beta-binomial-1
  left hand tail of Sinh-Arcsinh-1
  location of Cauchy-1
  location of Folded-Normal-1
  location of Generalized-Gamma-2
  location of Gumbel-1
  location of Half-normal-2
  location of Laplace-1
  location of Laplace-2
  location of Levy-1
  location of Logistic-1
  location of Logistic-2
  location of Logit-Normal-1
  location of Multivariate-Normal-1
  location of Multivariate-Normal-2
  location of Multivariate-Normal-3
  location of Multivariate-Student-T-1
  location of Multivariate-Student-T-2
  location of Normal-inverse-gamma-1
  location of Pareto-Type-II
  location of Power-Normal-1
  location of Sinh-Arcsinh-1
  location of Sinh-Arcsinh-2
  location of Skew-Normal
  location of Standard-Two-Sided-Power-1
  location of Two-Sided-Power-1
  location of Von-Mises-1
  location of minimum of Frechet-2
  location parameter of Amoroso-1
  location parameter of Asymmetric-Laplace-1
  location parameter of Johnson-SB-1
  location parameter of Johnson-SL-1
  location parameter of Johnson-SN-1
  location parameter of Johnson-SU-1
  log Poisson intensity of Poisson-2
  log mean of Negative-Binomial-6
  logit of probability of success of Bernoulli-2
  logit of success probability in each trial of Binomial-2
  lognormal
  lower bound of Arcsine-2
  lower bound of Truncated-Normal-1
  lower limit of Triangular-1
  lower triangular matrix of Multivariate-Gaussian-Process-Distribution-2
  lower triangular matrix of Multivariate-Normal-3
  maximum of Log-Uniform-1
  maximum of Standard-Uniform-1
  maximum of Uniform-1
  maximum of Uniform-Discrete-1
  mean of Arcsine 1
  mean of Arcsine 2
  mean of Asymmetric Laplace 1
  mean of Benford 1
  mean of Bernoulli 1
  mean of Beta 1
  mean of Beta Negative Binomial1
  mean of Beta-binomial 1
  mean of Binomial 1
  mean of Categorical Nonordered 1
  mean of Categorical Ordered 1
  mean of Cauchy 1
  mean of Chi 1
  mean of Chi-squared 1
  mean of Conway-Maxwell-Poisson 1
  mean of Dagum 1
  mean of Dirichlet 1
  mean of Double Poisson 1
  mean of Epanechnikov 1
  mean of Erlang 1
  mean of Exponential 1
  mean of Exponential 2
  mean of Exponentially modified Gaussian 1
  mean of Exponentially-modified-Gaussian-1
  mean of F 1
  mean of Folded Normal 1
  mean of Frechet 1
  mean of Frechet 2
  mean of Gamma 1
  mean of Gamma 2
  mean of Generalized Gamma 1
  mean of Generalized Gamma 2
  mean of Generalized Negative Binomial 1
  mean of Generalized Poisson 1
  mean of Generalized Poisson 3
  mean of Generalized-Poisson-3
  mean of GeneralizedPoisson2
  mean of GeneralizedPoisson2
  mean of Geometric 1
  mean of Gumbel 1
  mean of Half Cauchy 1
  mean of Half-normal 1
  mean of Half-normal 2
  mean of Hyperbolic secant 1
  mean of Hypergeometric 1
  mean of Inverse Binomial 1
  mean of Inverse Chi-Square
  mean of Inverse-Gamma 1
  mean of Inverse-Gaussian-1
  mean of Inverse-Wishart 1
  mean of Kumaraswamy 1
  mean of Laplace 1
  mean of Laplace 2
  mean of Levy 1
  mean of Log-Logistic 1
  mean of Log-Logistic 2
  mean of Log-Normal 1
  mean of Log-Normal 2
  mean of Log-Normal 3
  mean of Log-Normal 4
  mean of Log-Normal 5
  mean of Log-Normal 6
  mean of Log-Normal 7
  mean of Log-Uniform 1
  mean of Logistic 1
  mean of Logistic 2
  mean of Logit Normal 1
  mean of Lomax 1
  mean of Makeham 1
  mean of Maxwell Boltzmann 1
  mean of Multinomial 1
  mean of Multivariate Normal 1
  mean of Multivariate Normal 2
  mean of Multivariate Normal 3
  mean of Multivariate Student T 1
  mean of Muth 1
  mean of Nakagami 1
  mean of Negative Binomial 1
  mean of Negative Binomial 2
  mean of Negative Binomial 3
  mean of Negative Binomial 4
  mean of Negative Binomial 5
  mean of Negative Binomial 6
  mean of Negative-Binomial-3
  mean of Noncentral F 1
  mean of Noncentral chi-squared 1
  mean of NoncentralT
  mean of Normal 1
  mean of Normal 2
  mean of Normal 3
  mean of Normal-1
  mean of Normal-2
  mean of Normal-3
  mean of Pareto Type I
  mean of Poisson 1
  mean of Poisson 2
  mean of Power 1
  mean of Rayleigh 1
  mean of Scaled Inverse Chi-Square
  mean of Skew Normal
  mean of Standard Cauchy 1
  mean of Standard Logistic 1
  mean of Standard Normal 1
  mean of Standard Power 1
  mean of Standard Triangular 1
  mean of Standard Two-Sided Power 1
  mean of Standard Uniform 1
  mean of Standard-Normal-1
  mean of Student's t-distribution 1
  mean of Student's t-distribution 2
  mean of Student-s-t-distribution-2
  mean of Student-s-t-distribution-3
  mean of Trapezoidal 1
  mean of Triangular 1
  mean of Truncated Normal 1
  mean of Truncated-Normal-1
  mean of Two-Sided Power 1
  mean of Uniform 1
  mean of Uniform Discrete 1
  mean of Uniform Discrete 2
  mean of Von Mises 1
  mean of Weibull 1
  mean of Wigner Semicircle 1
  mean of Wishart 1
  mean of YuleSimon1
  mean of Zero-Inflated Generalized Poisson 1
  mean of Zero-Inflated Negative Binomial 1
  mean of Zero-Inflated-Generalized-Poisson-1
  mean of Zero-Inflated-Negative-Binomial-1
  mean of Zero-inflated Poisson 1
  mean of Zeta 1
  mean of Zipf 1
  mean of logx of Log-Normal-1
  mean of logx of Log-Normal-2
  mean of logx of Log-Normal-5
  mean of x of Log-Normal-7
  median / geometric mean of Log-Normal-3
  median / geometric mean of Log-Normal-4
  median / geometric mean of Log-Normal-6
  median of Arcsine 1
  median of Arcsine 2
  median of Benford 1
  median of Bernoulli 1
  median of Beta 1
  median of Binomial 1
  median of Categorical Nonordered 1
  median of Categorical Ordered 1
  median of Cauchy 1
  median of Chi-squared 1
  median of Conway-Maxwell-Poisson 1
  median of Dagum 1
  median of Exponential 1
  median of Exponential 2
  median of Frechet 1
  median of Frechet 2
  median of Gamma 1
  median of Geometric 1
  median of Gompertz 1
  median of Gumbel 1
  median of Half Cauchy 1
  median of Hyperbolic secant 1
  median of Kumaraswamy 1
  median of Laplace 1
  median of Levy 1
  median of Log-Logistic 1
  median of Log-Logistic 2
  median of Log-Normal 1
  median of Log-Normal 2
  median of Log-Normal 3
  median of Log-Normal 4
  median of Log-Normal 5
  median of Log-Normal 6
  median of Log-Normal 7
  median of Logistic 1
  median of Logistic 2
  median of Logit Normal 1
  median of Lomax 1
  median of Makeham 1
  median of Maxwell Boltzmann 1
  median of Multivariate Student T 1
  median of Nakagami 1
  median of Normal 1
  median of Normal 2
  median of Normal 3
  median of Pareto Type I
  median of Poisson 1
  median of Rayleigh 1
  median of Standard Cauchy 1
  median of Standard Logistic 1
  median of Standard Normal 1
  median of Standard Power 1
  median of Standard Triangular 1
  median of Standard Uniform 1
  median of Student's t-distribution 1
  median of Uniform 1
  median of Uniform Discrete 1
  median of Von Mises 1
  median of Weibull 1
  median of Wigner Semicircle 1
  minimum of Log-Uniform-1
  minimum of Standard-Uniform-1
  minimum of Uniform-1
  minimum of Uniform-Discrete-1
  mixing coefficients of Mixture-Distribution-1
  mode of Arcsine 1
  mode of Arcsine 2
  mode of Benford 1
  mode of Bernoulli 1
  mode of Beta 1
  mode of Binomial 1
  mode of Categorical Nonordered 1
  mode of Categorical Ordered 1
  mode of Cauchy 1
  mode of Chi 1
  mode of Chi-squared 1
  mode of Dagum 1
  mode of Dirichlet 1
  mode of Erlang 1
  mode of Exponential 1
  mode of Exponential 2
  mode of F 1
  mode of Frechet 1
  mode of Frechet 2
  mode of Gamma 1
  mode of Generalized Gamma 1
  mode of Generalized Gamma 2
  mode of Geometric 1
  mode of Gumbel 1
  mode of Hyperbolic secant 1
  mode of Hypergeometric 1
  mode of Inverse Chi-Square
  mode of Inverse-Gamma 1
  mode of Inverse-Wishart 1
  mode of Kumaraswamy 1
  mode of Laplace 1
  mode of Levy 1
  mode of Log-Logistic 1
  mode of Log-Normal 1
  mode of Log-Normal 2
  mode of Log-Normal 3
  mode of Log-Normal 4
  mode of Log-Normal 5
  mode of Log-Normal 6
  mode of Log-Normal 7
  mode of Logistic 1
  mode of Logistic 2
  mode of Logit Normal 1
  mode of Lomax 1
  mode of Makeham 1
  mode of Multivariate Normal 1
  mode of Multivariate Normal 2
  mode of Multivariate Normal 3
  mode of Multivariate Student T 1
  mode of Nakagami 1
  mode of Negative Binomial 1
  mode of Negative Binomial 4
  mode of Normal 1
  mode of Normal 2
  mode of Normal 3
  mode of Pareto Type I
  mode of Poisson 1
  mode of Rayleigh 1
  mode of Scaled Inverse Chi-Square
  mode of Standard Cauchy 1
  mode of Standard Logistic 1
  mode of Standard Normal 1
  mode of Standard Triangular 1
  mode of Standard Uniform 1
  mode of Student's t-distribution 1
  mode of Student's t-distribution 2
  mode of Triangular 1
  mode of Uniform 1
  mode of Von Mises 1
  mode of Weibull 1
  mode of Wigner Semicircle 1
  mode of Wishart 1
  mode of YuleSimon1
  noncentrality parameter of Noncentral-chi-squared-1
  noncentrality parameter of Noncentral-Beta-1
  noncentrality parameter of Noncentral-F-1
  noncentrality parameter of NoncentralT
  noncentrality parameter of Rice-1
  nondecision time of Wiener-Diffusion-Model-1
  number of elements of Zipf-1
  number of failures of Negative-Binomial-4
  number of successes of Beta-Negative-Binomial1
  number of successes of Hypergeometric-1
  number of successes of Negative-Binomial-1
  number of trials of Beta-binomial-1
  number of trials of Binomial-1
  number of trials of Binomial-2
  number of trials of Hypergeometric-1
  number of trials of Multinomial-1
  number of values of Uniform-Discrete-2
  ordered cutpoints of Ordered-Logistic-1
  overdispersion of Negative-Binomial-2
  overdispersion of Zero-Inflated-Negative-Binomial-1
  population size of Hypergeometric-1
  precision matrix of Multivariate-Normal-2
  precision matrix of Multivariate-Student-T-2
  precision of Laplace-2
  precision of Log-Normal-5
  precision of Normal-3
  predictor of Ordered-Logistic-1
  probability of Inverse-Binomial-1
  probability of extra zeros of Zero-inflated-Poisson-1
  probability of success of Bernoulli-1
  probability of zero of Zero-Inflated-Generalized-Poisson-1
  probability of zero of Zero-Inflated-Negative-Binomial-1
  radius of Wigner-Semicircle-1
  rate of Borel-1
  rate of Gamma-2
  rate of decay of Conway-Maxwell-Poisson-1
  rate or inverse scale of Exponential-1
  rate or inverse scale of Exponentially-modified-Gaussian-1
  relationship between Amoroso 1 and Chi 1 whereby \\text{Chi1}k \\text{ distribution is a special case of the Amoroso1} a,\\theta,\\alpha,\\beta \\text{ distribution when } a = 0, \\theta=\\sqrt{2}, \\alpha=k/2, \\beta=2
  relationship between Amoroso 1 and Chi-squared 1 whereby \\text{ChiSquared1}k \\text{ distribution is a special case of the Amoroso1} a,\\theta,\\alpha,\\beta \\text{ distribution when } a = 0, \\theta=2, \\alpha=k/2, \\beta=1
  relationship between Amoroso 1 and Frechet 1 whereby \\text{Frechet1}\\alpha,\\sigma \\text{ distribution is a special case of the Amoroso1} a,\\theta,\\alpha,\\beta \\text{ distribution when } a=0, \\theta=\\sigma, \\alpha=1, \\beta rightarrow -\\beta
  relationship between Amoroso 1 and Gamma 1 whereby \\text{Gamma1 distribution is a special case of the Amoroso1} a,\\theta,\\alpha,\\beta \\text{ distribution when} a = 0, \\beta=1
  relationship between Amoroso 1 and Half-normal 2 whereby \\text{HalfNormal2}\\mu,\\sigma \\text{ distribution is a special case of the Amoroso1} a,\\theta,\\alpha,\\beta \\text{ distribution for } \\mu=0 \\text{ and when } a = 0, \\theta=\\sqrt{2\\sigma^2}, \\alpha=1/2, \\beta=2
  relationship between Amoroso 1 and Inverse Chi-Square whereby \\text{InverseChiSquare1}k \\text{ distribution is a special case of the Amoroso1} a,\\theta,\\alpha,\\beta \\text{ distribution when } a = 0, \\theta=1/2, \\alpha=k/2, \\beta=-1
  relationship between Amoroso 1 and Levy 1 whereby \\text{Levy1}\\mu,c \\text{ distribution is a special case of the Amoroso1} a,\\theta,\\alpha,\\beta \\text{ distribution when } \\theta=c/2, \\alpha=1/2, \\beta=-1
  relationship between Amoroso 1 and Normal 1 whereby \\text{Normal1}\\mu,\\sigma \\text{ distribution is a special case of the Amoroso1} a,\\theta,\\alpha,\\beta \\text{ distribution when } a=\\mu-\\sigma\\sqrt{\\alpha}, \\theta=\\sigma/\\sqrt{\\alpha}, \\beta=1 \\text{ and } \\alpha \\rightarrow \\infty
  relationship between Amoroso 1 and Rayleigh 1 whereby \\text{Rayleigh1}\\sigma \\text{ distribution is a special case of the Amoroso1} a,\\theta,\\alpha,\\beta \\text{ distribution when } a = 0, \\theta=\\sqrt{2\\sigma^2}, \\alpha=1, \\beta=2
  relationship between Amoroso 1 and Weibull 1 whereby \\text{Weibull1}\\lambda,k \\text{ distribution is a special case of the Amoroso1} a,\\theta,\\alpha,\\beta \\text{ distribution when } a = 0, \\theta=\\lambda, \\alpha=1
  relationship between Arcsine 2 and Arcsine 1 whereby a=0, b=1
  relationship between Bernoulli 1 and Bernoulli 2 whereby \\alpha = \\logp/1-p
  relationship between Bernoulli 1 and Binomial 1 whereby \\Sigma X iid
  relationship between Bernoulli 2 and Bernoulli 1 whereby p = \\exp\\alpha / 1 + \\exp\\alpha
  relationship between Beta 1 and Arcsine 1 whereby \\alpha=1/2, \\beta = 1/2
  relationship between Beta 1 and Normal 1 whereby \\alpha = \\beta, \\beta \\rightarrow \\infty
  relationship between Beta 1 and Standard Uniform 1 whereby \\alpha=1, \\beta = 1
  relationship between Beta Negative Binomial1 and Negative Binomial 1 whereby \\text{If } X \\sim \\text{NegativeBinomial1n,p and } p \\sim \\text{Beta1}\\alpha,\\beta \\text{ then } X \\sim \\text{NegativeBinomial1}\\alpha,\\beta,n
  relationship between Beta-binomial 1 and Uniform Discrete 2 whereby \\alpha=1, \\beta=1
  relationship between Binomial 1 and Bernoulli 1 whereby n=1
  relationship between Binomial 1 and Binomial 2 whereby \\alpha = \\logp/1-p
  relationship between Binomial 1 and Normal 1 whereby \\text{For } X \\sim Binomial1n,p \\text{ as } n \\rightarrow \\infty, X \\text{ is approximately normally distributed } \\\\Normal1\\mu,\\sigma \\text{ with } \\mu=np, \\sigma=np1-p.
  relationship between Binomial 1 and Poisson 1 whereby \\lambda = np, n \\rightarrow \\infty
  relationship between Binomial 2 and Binomial 1 whereby p = \\exp\\alpha / 1 + \\exp\\alpha
  relationship between Cauchy 1 and Standard Cauchy 1 whereby x0=0, \\gamma=1
  relationship between Chi 1 and Chi-squared 1 whereby \\text{If }X \\sim Chi1k \\text{ then } X^2 \\sim ChiSquared1k
  relationship between Chi-squared 1 and Exponential 1 whereby k=2 \\text{ and } \\lambda=1/2
  relationship between Chi-squared 1 and F 1 whereby \\text{If } X_1 \\sim ChiSquared1n_1, X_2 \\sim ChiSquared1n_2 \\text{ are independent random variables }\\\\ \\Rightarrow \\frac{X_1/n_1}{X_2/n_2} \\sim F1n_1,n_2
  relationship between Conway-Maxwell-Poisson 1 and Binomial 1 whereby \\text{For } \\nu=\\infty \\text{ the distribution of the sum is binomial with parameters } \\\\ n \\text{ and } \\lambda/1+\\lambda
  relationship between Conway-Maxwell-Poisson 1 and Negative Binomial 1 whereby \\text{ For } \\nu=0 \\text{ and } \\lambda<1 \\text{ the sum of Conway-Maxwell-Poisson distributed variables}\\\\ \\text{reduces to the sum of geometric variables, which follows a Negative Binomial distribution with parameters}\\\\ n \\text{ and } 1-\\lambda
  relationship between Conway-Maxwell-Poisson 1 and Poisson 1 whereby \\text{For } \\nu = 1 \\text{ the sum has a Poisson distribution with parameter } n\\lambda
  relationship between Double Poisson 1 and Poisson 1 whereby \\phi=1
  relationship between Erlang 1 and Exponential 2 whereby c=1, b=\\beta
  relationship between Exponential 1 and Exponential 2 whereby \\beta=1/\\lambda
  relationship between Exponential 2 and Exponential 1 whereby \\lambda=1/\\beta
  relationship between Exponential 2 and F 1 whereby \\text{If } X_1, X_2 \\sim Exponential21 \\text{ mutually independent and identically distributed} \\\\ \\text{ random variables } \\Rightarrow X_1/X_2 \\text{ has the } F1 \\text{ distribution}
  relationship between F 1 and Chi-squared 1 whereby \\text{If } X \\sim F1n_1,n_2 \\text{, the limiting distribution of } n_1X \\text{ as } n_2 \\rightarrow \\infty \\text{ is} \\\\ \\text{ the chi-square distribution with } n_1 \\text{ degrees of freedom}
  relationship between Frechet 1 and Weibull 1 whereby X \\sim Frechet1\\alpha,\\sigma \\rightarrow X^{-1} \\sim Weibull\\lambda=1/\\sigma,k=\\alpha
  relationship between Frechet 2 and Frechet 1 whereby m=0
  relationship between Frechet 2 and Weibull 1 whereby X \\sim Frechet2\\alpha,\\sigma,m \\text{ with } m=0 \\rightarrow X^{-1} \\sim Weibull\\lambda=1/\\sigma,k=\\alpha
  relationship between Gamma 1 and Beta 1 whereby X1, X2 \\sim Gamma1k,\\theta \\text{ and } Y = X1/X1+X2 \\Rightarrow Y \\sim Beta1\\alpha,\\beta
  relationship between Gamma 1 and Chi-squared 1 whereby k_{ChiSquared1}=2k, \\theta=2
  relationship between Gamma 1 and Erlang 1 whereby k \\in N, k=c, \\theta=b
  relationship between Gamma 1 and Exponential 1 whereby k=1, \\theta=1/\\lambda
  relationship between Gamma 1 and Gamma 2 whereby r=k, \\mu = 1/ \\theta
  relationship between Gamma 1 and Inverse-Gamma 1 whereby \\text{If } X \\sim Gamma1\\alpha,\\beta \\text{ then } X^{-1} \\sim InverseGamma1\\alpha,\\beta^{-1}
  relationship between Gamma 1 and Normal 1 whereby \\mu = k \\theta, \\sigma^2 = k^2 \\theta, \\theta \\rightarrow \\infty
  relationship between Gamma 2 and Gamma 1 whereby k=r, \\theta = 1 / \\mu
  relationship between Generalized Gamma 1 and Gamma 1 whereby p=1, k=d, \\theta=a
  relationship between Generalized Gamma 1 and Generalized Gamma 3 whereby r=d/p, \\beta=p, \\mu = 1/a
  relationship between Generalized Gamma 2 and Chi-squared 1 whereby a=0, b=2, c=k_{ChiSquare1}/2,k=1
  relationship between Generalized Gamma 2 and Exponential 1 whereby k=c=1, a=0, b=1/\\lambda
  relationship between Generalized Gamma 2 and Gamma 1 whereby k=1, a=0 \\text{ and renaming parameters: } c=k, b=\\theta
  relationship between Generalized Gamma 2 and Generalized Gamma 1 whereby a = 0, kc=d, \\text{ and rename } k=p, b=a
  relationship between Generalized Gamma 2 and Weibull 1 whereby c=1, a=0, b=\\lambda
  relationship between Generalized Gamma 3 and Generalized Gamma 1 whereby a=1/\\mu, d=\\beta r, p=\\beta
  relationship between Generalized Negative Binomial 1 and Binomial 1 whereby \\beta=0 \\text{ and set } m=n, \\theta=p
  relationship between Generalized Negative Binomial 1 and Inverse Binomial 1 whereby \\beta=2, \\theta=1-p
  relationship between Generalized Negative Binomial 1 and Negative Binomial 4 whereby \\beta=1 \\text{ and set } m=r, \\theta=p
  relationship between Generalized Poisson 1 and GeneralizedPoisson2 whereby \\mu = \\theta / 1-\\delta
  relationship between Generalized Poisson 1 and Poisson 1 whereby \\delta = 0, \\theta=\\mu
  relationship between Generalized Poisson 3 and Poisson 1 whereby \\alpha = 0, \\lambda=\\mu
  relationship between GeneralizedPoisson2 and Generalized Poisson 1 whereby \\theta = \\mu 1-\\delta
  relationship between GeneralizedPoisson2 and Poisson 1 whereby \\delta = 0, \\lambda=\\mu
  relationship between Geometric 1 and Negative Binomial 1 whereby \\Sigma X iid
  relationship between Half-normal 2 and Half-normal 1 whereby \\mu=0, \\sigma=\\sqrt{\\pi} / \\theta \\sqrt{2}
  relationship between Hypergeometric 1 and Binomial 1 whereby p = K/N, n=n, N \\rightarrow \\infty
  relationship between Hypergeometric 1 and Normal 1 whereby X \\sim Hypergeometric1N, K, n \\Rightarrow Y\\sim Normal1\\mu,\\sigma \\text{ for large n, but K/N not too small}
  relationship between Hypergeometric 1 and Poisson 1 whereby X \\sim Hypergeometric1N, K, n \\Rightarrow Y\\sim Poisson1\\lambda \\text{ as K, N and n tend to infinity for } \\\\ K/N \\text{ small and } nK/N \\rightarrow \\lambda
  relationship between Inverse Gaussian 1 and Chi-squared 1 whereby X \\sim InverseGaussian1\\lambda,\\mu \\text{ and } Y = \\lambda X-\\mu^2 / \\mu^2 X \\Rightarrow Y \\sim ChiSquared1k
  relationship between Inverse Gaussian 1 and Standard Normal 1 whereby \\lambda \\rightarrow \\infty
  relationship between Kumaraswamy 1 and Exponential 1 whereby \\text{If } X \\sim Kumaraswamy11,b \\text{ then } -1-\\logX \\sim Exponential1b
  relationship between Kumaraswamy 1 and Exponential 1 whereby \\text{If } X \\sim Kumaraswamy1a,1 \\text{ then } -\\logX \\sim Exponential1a
  relationship between Kumaraswamy 1 and Standard Uniform 1 whereby \\text{If } X \\sim Kumaraswamy11,1 \\text{ then } X \\sim StandardUniform1
  relationship between Laplace 1 and Laplace 2 whereby \\tau=1/b
  relationship between Laplace 2 and Laplace 1 whereby b=1/\\tau
  relationship between Log-Logistic 1 and Log-Logistic 2 whereby \\lambda=1/\\alpha, \\kappa=\\beta
  relationship between Log-Logistic 1 and Logistic 1 whereby \\text{If } X \\sim LogLogistic1\\alpha,\\beta \\Rightarrow Y = logX \\sim Logistic1\\mu,s \\text{ with } \\mu=\\log\\alpha, s=1/\\beta
  relationship between Log-Logistic 2 and Log-Logistic 1 whereby \\alpha=1/\\lambda, \\beta=\\kappa
  relationship between Log-Normal 1 and Log-Normal 2 whereby \\mu = \\mu, v = \\sigma^2
  relationship between Log-Normal 1 and Log-Normal 3 whereby m = \\exp\\mu, \\sigma = \\sigma
  relationship between Log-Normal 1 and Log-Normal 4 whereby m = \\exp\\mu, cv = \\sqrt{\\exp\\sigma^2 - 1}
  relationship between Log-Normal 1 and Log-Normal 5 whereby \\mu = \\mu, \\tau = 1 / \\sigma^2
  relationship between Log-Normal 1 and Log-Normal 6 whereby m=\\exp\\mu, \\sigma_g=\\exp\\sigma
  relationship between Log-Normal 1 and Log-Normal 7 whereby \\mu_N = \\exp\\Big\\mu + \\frac12 \\sigma^2\\Big, \\sigma_N = \\exp\\big\\mu + \\frac{1}{2}\\sigma^2\\big\\sqrt{\\exp\\sigma^2-1}
  relationship between Log-Normal 1 and Normal 1 whereby \\logX
  relationship between Log-Normal 2 and Log-Normal 1 whereby \\mu = \\mu, \\sigma = \\sqrt{v}
  relationship between Log-Normal 2 and Log-Normal 3 whereby m = \\exp\\mu, \\sigma = \\sqrt{v}
  relationship between Log-Normal 2 and Log-Normal 4 whereby m = \\exp\\mu, cv = \\sqrt{\\expv - 1}
  relationship between Log-Normal 2 and Log-Normal 5 whereby \\mu = \\mu, \\tau = 1 / v
  relationship between Log-Normal 2 and Log-Normal 6 whereby m=\\exp\\mu, \\sigma_g=\\exp\\sqrt{v}
  relationship between Log-Normal 2 and Log-Normal 7 whereby \\mu_N = \\exp\\mu+v/2, \\sigma_N = \\exp\\mu+v/2\\sqrt{\\expv-1}
  relationship between Log-Normal 3 and Log-Normal 1 whereby \\mu = \\logm, \\sigma = \\sigma
  relationship between Log-Normal 3 and Log-Normal 2 whereby \\mu = \\logm, v = \\sigma^2
  relationship between Log-Normal 3 and Log-Normal 4 whereby m = m, cv = \\sqrt{\\exp\\sigma^2 - 1}
  relationship between Log-Normal 3 and Log-Normal 5 whereby \\mu = \\logm, \\tau = 1 / \\sigma^2
  relationship between Log-Normal 3 and Log-Normal 6 whereby m = m, \\sigma_g=\\exp\\sigma
  relationship between Log-Normal 3 and Log-Normal 7 whereby \\mu_N = m\\;\\exp\\sigma^2/2, \\sigma_N = m \\;\\exp\\sigma^2/2\\sqrt{\\exp\\sigma^2-1}
  relationship between Log-Normal 4 and Log-Normal 1 whereby \\mu = \\logm, \\sigma = \\sqrt{\\logcv^2+1}
  relationship between Log-Normal 4 and Log-Normal 2 whereby \\mu = \\logm, v = \\logcv^2+1
  relationship between Log-Normal 4 and Log-Normal 3 whereby m = m, \\sigma = \\sqrt{\\logcv^2+1}
  relationship between Log-Normal 4 and Log-Normal 5 whereby \\mu = \\logm, \\tau = 1 / \\logcv^2 + 1
  relationship between Log-Normal 4 and Log-Normal 6 whereby m = m, \\sigma_g=\\exp\\!\\big\\sqrt{\\logcv^2+1}\\big
  relationship between Log-Normal 4 and Log-Normal 7 whereby \\mu_N = m \\sqrt{cv^2 + 1}, \\sigma_N = m \\;cv\\,\\sqrt{cv^2 + 1}
  relationship between Log-Normal 5 and Log-Normal 1 whereby \\mu = \\mu, \\sigma = 1 / \\sqrt{\\tau}
  relationship between Log-Normal 5 and Log-Normal 2 whereby \\mu = \\mu, v = 1 / \\tau
  relationship between Log-Normal 5 and Log-Normal 3 whereby m = \\exp\\mu, \\sigma = 1 / \\sqrt{\\tau}

Ontology information

Ontology ID: probonto
Version: 2.5.0
Number of terms: 39
Last loaded: Wed May 17 12:18:40 BST 2017