nag_rand_students_t (g05snc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rand_students_t (g05snc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_students_t (g05snc) 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_rand_students_t (Integer n, Integer df, Integer state[], double x[], NagError *fail)

3  Description

The distribution has PDF (probability density function)
fx= ν-12 ! 12ν-1!πν 1+x2ν 12ν+1 .
nag_rand_students_t (g05snc) calculates the values
yiνzi,   i= 1,,n
where the yi are generated by nag_rand_normal (g05skc) with mean 0 and variance 1.0, and the zi are generated by nag_rand_gamma (g05sjc) with parameters 12ν and 2 (i.e., from a χ2-distribution with ν degrees of freedom).
One of the initialization functions nag_rand_init_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_students_t (g05snc).

4  References

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

5  Arguments

1:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2:     dfIntegerInput
On entry: ν, the number of degrees of freedom of the distribution.
Constraint: df1 .
3:     state[dim]IntegerCommunication Array
Note: the actual argument supplied must be the array state supplied to the initialization functions nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
4:     x[n]doubleOutput
On exit: the n pseudorandom numbers from the specified Student's t-distribution.
5:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, df=value.
Constraint: df1.
On entry, n=value.
Constraint: n0.
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_INVALID_STATE
On entry, state vector has been corrupted or not initialized.

7  Accuracy

Not applicable.

8  Further Comments

The time taken by nag_rand_students_t (g05snc) 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_rand_students_t (g05snc), after initialization by nag_rand_init_repeatable (g05kfc).

9.1  Program Text

Program Text (g05snce.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05snce.r)


nag_rand_students_t (g05snc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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