NAG C Library Function Document

nag_prob_beta_vector (g01sec)

1
Purpose

nag_prob_beta_vector (g01sec) computes a number of lower or upper tail probabilities for the beta distribution.

2
Specification

#include <nag.h>
#include <nagg01.h>
void  nag_prob_beta_vector (Integer ltail, const Nag_TailProbability tail[], Integer lbeta, const double beta[], Integer la, const double a[], Integer lb, const double b[], double p[], Integer ivalid[], NagError *fail)

3
Description

The lower tail probability, P Bi βi :ai,bi  is defined by
P Bi βi :ai,bi = Γ ai + bi Γ ai Γ bi 0 βi Bi ai-1 1-Bi bi-1 dBi = Iβi ai,bi ,   0 βi 1 ;  ai , bi > 0 .  
The function Iβiai,bi, also known as the incomplete beta function is calculated using nag_incomplete_beta (s14ccc).
The input arrays to this function are designed to allow maximum flexibility in the supply of vector arguments by re-using elements of any arrays that are shorter than the total number of evaluations required. See Section 2.6 in the g01 Chapter Introduction for further information.

4
References

NIST Digital Library of Mathematical Functions
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth
Majumder K L and Bhattacharjee G P (1973) Algorithm AS 63. The incomplete beta integral Appl. Statist. 22 409–411

5
Arguments

1:     ltail IntegerInput
On entry: the length of the array tail.
Constraint: ltail>0.
2:     tail[ltail] const Nag_TailProbabilityInput
On entry: indicates whether a lower or upper tail probabilities are required. For j= i-1 mod ltail , for i=1,2,,maxltail,lbeta,la,lb:
tail[j]=Nag_LowerTail
The lower tail probability is returned, i.e., pi = P Bi βi :ai,bi .
tail[j]=Nag_UpperTail
The upper tail probability is returned, i.e., pi = P Bi βi :ai,bi .
Constraint: tail[j-1]=Nag_LowerTail or Nag_UpperTail, for j=1,2,,ltail.
3:     lbeta IntegerInput
On entry: the length of the array beta.
Constraint: lbeta>0.
4:     beta[lbeta] const doubleInput
On entry: βi, the value of the beta variate with βi=beta[j], j=i-1 mod lbeta.
Constraint: 0.0beta[j-1]1.0, for j=1,2,,lbeta.
5:     la IntegerInput
On entry: the length of the array a.
Constraint: la>0.
6:     a[la] const doubleInput
On entry: ai, the first parameter of the required beta distribution with ai=a[j], j=i-1 mod la.
Constraint: a[j-1]>0.0, for j=1,2,,la.
7:     lb IntegerInput
On entry: the length of the array b.
Constraint: lb>0.
8:     b[lb] const doubleInput
On entry: bi, the second parameter of the required beta distribution with bi=b[j], j=i-1 mod lb.
Constraint: b[j-1]>0.0, for j=1,2,,lb.
9:     p[dim] doubleOutput
Note: the dimension, dim, of the array p must be at least maxltail,lbeta,la,lb.
On exit: pi, the probabilities for the beta distribution.
10:   ivalid[dim] IntegerOutput
Note: the dimension, dim, of the array ivalid must be at least maxltail,lbeta,la,lb.
On exit: ivalid[i-1] indicates any errors with the input arguments, with
ivalid[i-1]=0
No error.
ivalid[i-1]=1
On entry,invalid value supplied in tail when calculating pi.
ivalid[i-1]=2
On entry,βi<0.0,
orβi>1.0.
ivalid[i-1]=3
On entry,ai0.0,
orbi0.0,
11:   fail NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6
Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
NE_ARRAY_SIZE
On entry, array size=value.
Constraint: la>0.
On entry, array size=value.
Constraint: lb>0.
On entry, array size=value.
Constraint: lbeta>0.
On entry, array size=value.
Constraint: ltail>0.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
NW_IVALID
On entry, at least one value of beta, a, b or tail was invalid.
Check ivalid for more information.

7
Accuracy

The accuracy is limited by the error in the incomplete beta function. See Section 7 in nag_incomplete_beta (s14ccc) for further details.

8
Parallelism and Performance

nag_prob_beta_vector (g01sec) is not threaded in any implementation.

9
Further Comments

None.

10
Example

This example reads values from a number of beta distributions and computes the associated lower tail probabilities.

10.1
Program Text

Program Text (g01sece.c)

10.2
Program Data

Program Data (g01sece.d)

10.3
Program Results

Program Results (g01sece.r)