5.5 betainc_vec

: betainc_vec (x, a, b)

: betainc_vec (x, a, b, tail)

Compute the incomplete beta function ratio.

This function shadows the core function betainc. Performance improvement due to vectorized C++. Support for single precision was removed.

This is defined as

               x
              /
             |
I_x (a, b) = | t^(a-1) (1-t)^(b-1) dt
             |
             /
            0

with x real in [0,1], a and b real and strictly positive. If one of the input has more than one components, then the others must be scalar or of compatible dimensions.

By default or if tail is "lower" the incomplete beta function ratio integrated from 0 to x is computed. If tail is "upper" then the complementary function integrated from x to 1 is calculated. The two choices are related as

betainc (x, a, b, "lower") = 1 - betainc (x, a, b, "upper").

Reference

A. Cuyt, V. Brevik Petersen, B. Verdonk, H. Waadeland, W.B. Jones Handbook of Continued Fractions for Special Functions, ch. 18.

See also: beta, betaincinv, betaln.