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...

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

{\displaystyle \beta =1/\theta } ⁠, called a rate parameter. In each of these forms, both parameters are positive real numbers. The distribution has important...

In probability and statistics, the generalized beta distribution is a continuous probability distribution with four shape parameters (however it's customary...

the Beta distribution as a conjugate prior distribution. When using a general Beta ⁡ ( α , β ) {\displaystyle \operatorname {Beta} (\alpha ,\beta )} as...

distributions parameterized by a vector α {\displaystyle {\boldsymbol {\alpha }}} of positive reals. It is a multivariate generalization of the beta distribution...

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

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

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...

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

{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...

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

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

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

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

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

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

\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}...

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...

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

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...

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

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

^{-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...

{\displaystyle \beta =1} , the distribution is supported on [μ, ∞). The parameter c > 0 is a scale factor which is a measure of the width of the distribution while...

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

the distribution. The parameter β > 0 {\displaystyle \beta >0} is a shape parameter. The distribution is unimodal when β > 1 {\displaystyle \beta >1}...

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

categorical distribution is the generalization of the Bernoulli distribution for variables with any constant number of discrete values. The Beta distribution is...