nag_prob_beta_vector (g01sec) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_prob_beta_vector (g01sec)

+ Contents

    1  Purpose
    7  Accuracy

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

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
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:     ltailIntegerInput
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:     lbetaIntegerInput
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:     laIntegerInput
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:     lbIntegerInput
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:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
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.
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  Further Comments

None.

9  Example

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

9.1  Program Text

Program Text (g01sece.c)

9.2  Program Data

Program Data (g01sece.d)

9.3  Program Results

Program Results (g01sece.r)


nag_prob_beta_vector (g01sec) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012