### 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