nag_log_beta (s14cbc) (PDF version)
s Chapter Contents
s Chapter Introduction
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 ;
where
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

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.
NE_REAL
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

None.

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