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

as the beta distribution of the first kind, whereas beta distribution of the second kind is an alternative name for the beta prime distribution. The generalization...

{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...

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

degenerate distribution — but the notation treats it as if it were a continuous distribution. The Beta prime distribution The Birnbaum–Saunders distribution, also...

}.} The Lomax distribution with scale parameter λ = 1 is a special case of the beta prime distribution. If X has a Lomax distribution, then X λ ∼ β ′...

{\displaystyle \lambda '} denotes the Beta prime distribution. If the shape parameter of the gamma distribution is known, but the inverse-scale parameter...

years. His 1901 paper introduced the inverse-gamma distribution (type V) and the beta prime distribution (type VI). A Pearson density p is defined to be...

follows the Beta Prime distribution: f β ′ ( r , α , β ) = B ( α , β ) − 1 r α − 1 ( 1 + r ) − ( α + β ) {\displaystyle f_{\beta '}(r,\alpha ,\beta )=B(\alpha...

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

\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}...

Exponential family: Conjugate distributions. Beta-binomial distribution Denoted by the same symbols as the prior hyperparameters with primes added ('). For instance...

the spherical distribution assumption, can be derived from the Beta Prime distribution. If Z ∼ β ′ ( a , b ) {\displaystyle Z\sim \beta '(a,b)} then E...

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

{LL}}(\gamma ,\sigma )\sim \beta '(1,1,\gamma ,\sigma )} (Beta prime distribution). If X has a log-logistic distribution with scale parameter α {\displaystyle...

incomplete beta function Beta negative binomial distribution Beta prime distribution Beta rectangular distribution Beverton–Holt model Bhatia–Davis inequality...

three-parameter beta prime distribution. Compounding a half-normal distribution with its scale parameter distributed according to a Rayleigh distribution yields...

The Dagum distribution (or Mielke Beta-Kappa distribution) is a continuous probability distribution defined over positive real numbers. It is named after...

inverted Dirichlet distribution is a multivariate generalization of the beta prime distribution, and is related to the Dirichlet distribution. It was first...

the Poisson distribution is the gamma distribution. Let λ ∼ G a m m a ( α , β ) {\displaystyle \lambda \sim \mathrm {Gamma} (\alpha ,\beta )} denote that...

space of (all) distributions on U {\displaystyle U} , usually denoted by D ′ ( U ) {\displaystyle {\mathcal {D}}'(U)} (note the prime), which by definition...

typically three Tracy–Widom distributions, F β {\displaystyle F_{\beta }} , with β ∈ { 1 , 2 , 4 } {\displaystyle \beta \in \{1,2,4\}} . They correspond...

statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional...

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...

Alternating factorial Antichain Beta function Bhargava factorial Binomial coefficient Pascal's triangle Binomial distribution Binomial proportion confidence...

the space of distributions on U {\displaystyle U} and is denoted by D ′ ( U ) := ( C c ∞ ( U ) ) b ′ , {\displaystyle {\mathcal {D}}^{\prime }(U):=\left(C_{c}^{\infty...

Ariel 1 were used to measure distribution of the radiation produced by the tests. In 1963, it was reported that Starfish Prime had created a belt of MeV...

zero (see Bernoulli distribution). We wish to find the values of ⁠ β 0 {\displaystyle \beta _{0}} ⁠ and ⁠ β 1 {\displaystyle \beta _{1}} ⁠ which give the...

β z − 1 ) − 1 {\displaystyle n_{\rm {B}}(z)=(e^{\beta z}-1)^{-1}} is the Bose–Einstein distribution function. The case is similar for fermion frequencies...

{\hat {\beta }}})^{\prime }\mathbf {Q} ^{\prime }\mathbf {Q} (\mathbf {b} -{\boldsymbol {\hat {\beta }}})={\frac {p}{n-p}}(\mathbf {Z} ^{\prime }\mathbf...