Module beta

Provides the beta and related 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.