Beta inverse cumulative distribution function
x = betaincinv(y,z,w)
x = betaincinv(y,z,w,tail)
x = betaincinv(y,z,w) computes the inverse incomplete beta function for corresponding elements of y, z, and w, such that y = betainc(x,z,w). The elements of y must be in the closed interval [0,1], and those of z and w must be nonnegative. y, z, and w must all be real and the same size (or any of them can be scalar).
x = betaincinv(y,z,w,tail) specifies the tail of the incomplete beta function. Choices are 'lower' (the default) to use the integral from 0 to x, or 'upper' to use the integral from x to 1. These two choices are related as follows: betaincinv(y,z,w,'upper') = betaincinv(1-y,z,w,'lower'). When y is close to 0, the 'upper' option provides a way to compute x more accurately than by subtracting from y from 1.
The incomplete beta function is defined as
betaincinv computes the inverse of the incomplete beta function with respect to the integration limit x using Newton's method.