# Ncbetacdf

Ncbetacdf-func

## Definition:

computes the cdf with the lower tail of the non-central beta distribution. The lower tail probability for the non-central beta distribution with shape parameters and and non-centrality parameter , is defined by:

where

which is the central beta probability function or incomplete beta function.

## Parameters:

- (intput, double)
- the deviate, ,from the beta distribution, for which , is to be found.
- (input, double)
- the first shape parameter, a, of the required beta distribtution.
- (input, double)
- the second shape parameter, b, of the required beta distribtution.

- (input, double)
- the non-centrality parameter, , of the required beta distribution, , where is the safe range parameters as defined by NAG nag_real_safe_small_number (X02AMC). See chapter X02 in the NAG documentation.
- (output,double)
- the probability.