`betainc`

Regularized incomplete beta function.

Category: Mathematics > Elementary Math

Syntax

I = betainc(X, Z, W)

Returns the lower regularized incomplete beta function I_X(Z, W).

I = betainc(X, Z, W, tail)

Chooses 'lower' (default) or 'upper' tail.

Description

betainc(X, Z, W) is the integral of the beta density from 0 to X, so it is the cumulative distribution function of a beta random variable. It increases from 0 at X = 0 to 1 at X = 1. The upper tail option computes 1 - I directly and keeps accuracy when I is close to 1.

Input arguments

X: Values in the interval [0, 1].
Z, W: Positive shape parameters.
tail: 'lower' or 'upper'.

Output arguments

I: Values in [0, 1]. The upper tail equals 1 - lower.

Example

Cumulative beta distribution

betainc(0.5, 2, 3)
betainc(0.5, 2, 3, 'upper')
betainc(0.2, [1 2], 3)

Output

ans = 0.6875
ans = 0.3125
ans = 1×2

    0.4880    0.1808

See also

beta betaincinv betaln gammainc