probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1)...

probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers...

multivariate probability distributions parameterized by a vector α of positive reals. It is a multivariate generalization of the beta distribution, hence its alternative...

probability theory and statistics, the beta prime distribution (also known as inverted beta distribution or beta distribution of the second kind) is an absolutely...

respectively. Beta distribution and Beta prime distribution, two probability distributions related to the beta function Jacobi sum, the analogue of the beta function...

generalized beta distribution is a continuous probability distribution with four shape parameters, including more than thirty named distributions as limiting...

to the cumulative distribution functions of the beta distribution and of the F-distribution: F ( k ; n , p ) = F beta-distribution ( x = 1 − p ; α = n...

called the skew-logistic distribution. Type IV subsumes the other types and is obtained when applying the logit transform to beta random variates. Following...

(\lambda ;\alpha ,\beta )={\frac {\beta ^{\alpha }}{\Gamma (\alpha )}}\lambda ^{\alpha -1}\exp(-\lambda \beta ).} The posterior distribution p can then be...

Yes/No experiments all with the same probability of success. The beta-binomial distribution, which describes the number of successes in a series of independent...

{d_{2}}{2}}\right)}}.} The F-distribution is a particular parametrization of the beta prime distribution, which is also called the beta distribution of the second kind...

In probability theory, a beta negative binomial distribution is the probability distribution of a discrete random variable  X {\displaystyle X} equal...

\beta )=e^{-e^{-(x-\mu )/\beta }}\,} The standard Gumbel distribution is the case where μ = 0 {\displaystyle \mu =0} and β = 1 {\displaystyle \beta =1}...

β ) {\displaystyle \mathrm {Beta} (\alpha ,\beta )} distribution is α α + β {\displaystyle {\frac {\alpha }{\alpha +\beta }}} ,: 145  as α {\displaystyle...

statistics, the beta rectangular distribution is a probability distribution that is a finite mixture distribution of the beta distribution and the continuous...

{\displaystyle \beta =1} would give a uniform distribution) and B ( α , β ) {\displaystyle \mathrm {B} (\alpha ,\beta )} is the Beta function acting as...

probability distributions. For example, if one uses a beta distribution to model the distribution of the parameter p of a Bernoulli distribution, then: p...

{\displaystyle f(x;\alpha ,\beta )={\frac {f(x/\beta ;\alpha ,1)}{\beta }}} The cumulative distribution function is the regularized gamma function F (...

exists for this distribution H 1 − X = β − 1 α + β − 1  conditional on  β > 1 & α > 0 {\displaystyle H_{1-X}={\frac {\beta -1}{\alpha +\beta -1}}{\text{ conditional...

continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment...

positive imaginary part. The Wigner distribution coincides with a scaled and shifted beta distribution: if Y is a beta-distributed random variable with parameters...

within ( 0 , 1 ) {\displaystyle (0,1)} and can be assumed to follow a beta distribution. It is generalisable to variables which takes values in the arbitrary...

noncentral beta distribution is a continuous probability distribution that is a noncentral generalization of the (central) beta distribution. The noncentral...

chi-squared distribution Student's t-distribution can be obtained from chi-squared distribution and normal distribution The noncentral beta distribution can be...

bounded distribution is a family of continuous probability distributions defined on the interval (0,1). It is similar to the beta distribution, but much...

^{-1}+1}}\sim \beta (\beta ,\alpha )} 1 + Y ∼ { β ( β , α ) } − 1 {\displaystyle 1+\mathbf {Y} \sim \{\;\beta (\beta ,\alpha )\;\}^{-1}} , the distribution of the...

product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given...

now known as the beta distribution had been used by Thomas Bayes as a posterior distribution of the parameter of a Bernoulli distribution in his 1763 work...

In statistics, the matrix variate beta distribution is a generalization of the beta distribution. If U {\displaystyle U} is a p × p {\displaystyle p\times...

inexpensive distribution of software, companies have begun to take a looser approach to the use of the word beta. Developers may release either a closed beta, or...