nag_rngs_students_t (g05lbc) (PDF version)
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g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rngs_students_t (g05lbc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rngs_students_t (g05lbc) generates a vector of pseudorandom numbers taken from a Student's t-distribution with ν degrees of freedom.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rngs_students_t (Integer df, Integer n, double x[], Integer igen, Integer iseed[], NagError *fail)

3  Description

The distribution has PDF (probability density function)
fx= ν-12 ! 12ν-1!πν 1+x2ν 12ν+1 .
nag_rngs_students_t (g05lbc) calculates the values
yiνzi,   i= 1,,n
where the yi are generated by nag_rngs_normal (g05lac) from a Normal distribution with mean 0 and variance 1.0, and the zi are generated by nag_rngs_gamma (g05lfc) from a gamma distribution with parameters 12ν and 2 (i.e., from a χ2-distribution with ν degrees of freedom).
One of the initialization functions nag_rngs_init_repeatable (g05kbc) (for a repeatable sequence if computed sequentially) or nag_rngs_init_nonrepeatable (g05kcc) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_students_t (g05lbc).

4  References

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

5  Arguments

1:     dfIntegerInput
On entry: ν, the number of degrees of freedom of the distribution.
Constraint: df1 .
2:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
3:     x[n]doubleOutput
On exit: the n pseudorandom numbers from the specified Student's t-distribution.
4:     igenIntegerInput
On entry: must contain the identification number for the generator to be used to return a pseudorandom number and should remain unchanged following initialization by a prior call to nag_rngs_init_repeatable (g05kbc) or nag_rngs_init_nonrepeatable (g05kcc).
5:     iseed[4]IntegerCommunication Array
On entry: contains values which define the current state of the selected generator.
On exit: contains updated values defining the new state of the selected generator.
6:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument value had an illegal value.
On entry, df=value.
Constraint: df1.
On entry, n=value.
Constraint: n0.
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.

7  Accuracy

Not applicable.

8  Further Comments

The time taken by nag_rngs_students_t (g05lbc) increases with ν.

9  Example

This example prints five pseudorandom numbers from a Student's t-distribution with five degrees of freedom, generated by a single call to nag_rngs_students_t (g05lbc), after initialization by nag_rngs_init_repeatable (g05kbc).

9.1  Program Text

Program Text (g05lbce.c)

9.2  Program Data


9.3  Program Results

Program Results (g05lbce.r)

nag_rngs_students_t (g05lbc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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