# Ngl.betainc

Evaluates the incomplete beta function.

*Available in version 1.3.0 or later.*

## Prototype

alpha = Ngl.betainc(x, a, b)

## Arguments

*x*

Numpy or masked array representing upper limit of integration.
*x* must be [0,1].

*a*

First beta distribution parameter; must be > 0.0, and the same
dimensionality as *x*.

*b*

Second beta distribution parameter; must be > 0.0, and the same
dimensionality as *x*.

## Return value

*alpha*

An numpy or masked array is returned (depending on type of
*x*), of the same size as *x*. If *x*
is a masked array, then *alpha* will contain
missing values in the same locations.

## Description

**Ngl.betainc** calculates the
incomplete beta function. The incomplete beta function ratio is the
probability that a random variable from a beta distribution having
parameters *a* and *b* will be less than or equal to
*x*. The code used is from SLATEC (http://www.netlib.org/slatec/fnlib/). This
returns the same answers as the * Numerical Recipes * [Cambridge
Univ. Press, 1986] function *betai*.

This function is often used to determine probabilities.

## Examples

**Example 1**

import Ngl a = 0.5 b = 5.0 x = 0.2 alpha =The result is:Ngl.betainc(x,a,b) print "alpha(x,a,b) = ",alpha x = 0.5 alpha =Ngl.betainc(x,a,b) print "alpha(x,a,b) = ",alpha

alpha(x,a,b) = [ 0.85507239] alpha(x,a,b) = [ 0.98988044]

**Example 2**

This function can be used as a
p-Value
calculator for the Student t-test. Let's say a calculation has
been made where the degrees-of-freedom (`df`=20) and a
Student-t value of 2.08 has been determined. A probability level may
be determined via:

import Ngl df = 20 tval = 2.08 prob =Ngl.betainc( df/(df+tval^2), df/2.0, 0.5) print "prob=",prob

The result is `prob` = 0.0506. This is a two-tailed
probability. The one-tailed probability is 0.5*`prob` = 0.0253.

For plotting, users often prefer to plot the quantity:

prob = (1.-Ngl.betainc(x,a,b))*100. ; probability in %