| 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)). |