# BetaIaInv

## BetaIaInv(p, x, b)

Computes the inverse of the incomplete beta function, BetaI(p, a, b) with respect to «a». In other words, BetaIaInv returns a value such that BetaI(p, BetaIaInv(p, x, b), b) is equal to «x».

Note that this is similar to the BetaIInv(y, a, b) function, except that BetaIInv inverts BetaI with respect to the first parameter, «p», whereas BetaIaInv inverts it relative to the second parameter, «a».

The BetaIaInv function is closely related to the CumNegativeBinomInv function, which computes the inverse cumulative probability for a NegativeBinomial distribution. The two are related as:

CumNegativeBinomInv(u, r, p) + 1 = BetaIaInv(p, 1 - u, r)