# Package com.numericalmethod.suanshu.analysis.function.special.beta

• Class Summary
Class Description
Beta
The beta function defined as: $B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}= \int_0^1t^{x-1}(1-t)^{y-1}\,dt, x > 0, y > 0$

The R equivalent function is beta.

BetaRegularized
The Regularized Incomplete Beta function is defined as: $I_x(p,q) = \frac{B(x;\,p,q)}{B(p,q)} = \frac{1}{B(p,q)} \int_0^x t^{p-1}\,(1-t)^{q-1}\,dt, p > 0, q > 0$

The R equivalent function is pbeta.

BetaRegularizedInverse
The inverse of the Regularized Incomplete Beta function is defined at: $x = I^{-1}_{(p,q)}(u), 0 \le u \le 1$

The R equivalent function is qbeta.

LogBeta
This class represents the log of Beta function log(B(x, y)).
MultinomialBetaFunction
A multinomial Beta function is defined as: $\frac{\prod_{i=1}^K \Gamma(\alpha_i)}{\Gamma\left(\sum_{i=1}^K \alpha_i\right)},\qquad\boldsymbol{\alpha}=(\alpha_1,\cdots,\alpha_K)$