nag_log_beta (s14cbc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_log_beta (s14cbc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_log_beta (s14cbc) returns the value of the logarithm of the beta function, lnBa,b, via the routine name.

2  Specification

#include <nag.h>
#include <nags.h>
double  nag_log_beta (double a, double b, NagError *fail)

3  Description

nag_log_beta (s14cbc) calculates values for lnBa,b where B is the beta function given by
Ba,b = 0 1 ta-1 1-t b-1 dt
or equivalently
Ba,b = Γa Γb Γa+b
and Γx is the gamma function. Note that the beta function is symmetric, so that Ba,b=Bb,a.
In order to efficiently obtain accurate results several methods are used depending on the parameters a and b.
Let a0=mina,b and b0=maxa,b. Then:
for a08,
lnB = 0.5 ln 2π -0.5 lnb0 + Δa0 + Δ b0 - Δ a0+b0 - u - v ;
for a0<1,
for 2<a0<8,  a0 is reduced to the interval 1,2 by Ba,b=a0-1a0+b0-1 Ba0-1,b0;
for 1a02,
nag_log_beta (s14cbc) is derived from BETALN in DiDonato and Morris (1992).

4  References

DiDonato A R and Morris A H (1992) Algorithm 708: Significant digit computation of the incomplete beta function ratios ACM Trans. Math. Software 18 360–373

5  Arguments

1:     adoubleInput
On entry: the parameter a of the function.
Constraint: a>0.0.
2:     bdoubleInput
On entry: the parameter b of the function.
Constraint: b>0.0.
3:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

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.
On entry, a=value.
Constraint: a>0.0.
On entry, b=value.
Constraint: b>0.0.

7  Accuracy

nag_log_beta (s14cbc) should produce full relative accuracy for all input arguments.

8  Further Comments


9  Example

This example reads values of the parameters a and b from a file, evaluates the function and prints the results.

9.1  Program Text

Program Text (s14cbce.c)

9.2  Program Data

Program Data (s14cbce.d)

9.3  Program Results

Program Results (s14cbce.r)

nag_log_beta (s14cbc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

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