Module rgsl::gamma_beta::incomplete_beta

source ·

Functions

beta_inc
This routine computes the normalized incomplete Beta function I_x(a,b)=B_x(a,b)/B(a,b) where B_x(a,b) = \int_0^x t^{a-1} (1-t)^{b-1} dt for 0 <= x <= 1. For a > 0, b > 0 the value is computed using a continued fraction expansion. For all other values it is computed using the relation I_x(a,b,x) = (1/a) x^a 2F1(a,1-b,a+1,x)/B(a,b).
beta_inc_e
This routine computes the normalized incomplete Beta function I_x(a,b)=B_x(a,b)/B(a,b) where B_x(a,b) = \int_0^x t^{a-1} (1-t)^{b-1} dt for 0 <= x <= 1. For a > 0, b > 0 the value is computed using a continued fraction expansion. For all other values it is computed using the relation I_x(a,b,x) = (1/a) x^a 2F1(a,1-b,a+1,x)/B(a,b).