Module beta

Provides the beta and related function

Enums

BetaFuncError

Represents the errors that can occur when computing the natural logarithm of the beta function or the regularized lower incomplete beta function.

Functions

beta

Computes the beta function where a is the first beta parameter and b is the second beta parameter.

beta_inc

Computes the lower incomplete (unregularized) beta function B(a,b,x) = int(t^(a-1)*(1-t)^(b-1),t=0..x) for a > 0, b > 0, 1 >= x >= 0 where a is the first beta parameter, b is the second beta parameter, and x is the upper limit of the integral

beta_reg

Computes the regularized lower incomplete beta function I_x(a,b) = 1/Beta(a,b) * int(t^(a-1)*(1-t)^(b-1), t=0..x) a > 0, b > 0, 1 >= x >= 0 where a is the first beta parameter, b is the second beta parameter, and x is the upper limit of the integral.

checked_beta

Computes the beta function where a is the first beta parameter and b is the second beta parameter.

checked_beta_inc

Computes the lower incomplete (unregularized) beta function B(a,b,x) = int(t^(a-1)*(1-t)^(b-1),t=0..x) for a > 0, b > 0, 1 >= x >= 0 where a is the first beta parameter, b is the second beta parameter, and x is the upper limit of the integral

checked_beta_reg

Computes the regularized lower incomplete beta function I_x(a,b) = 1/Beta(a,b) * int(t^(a-1)*(1-t)^(b-1), t=0..x) a > 0, b > 0, 1 >= x >= 0 where a is the first beta parameter, b is the second beta parameter, and x is the upper limit of the integral.

checked_ln_beta

Computes the natural logarithm of the beta function where a is the first beta parameter and b is the second beta parameter and a > 0, b > 0.

inv_beta_reg

Computes the inverse of the regularized incomplete beta function

ln_beta

Computes the natural logarithm of the beta function where a is the first beta parameter and b is the second beta parameter and a > 0, b > 0.