One of the initialization functions nag_rand_init_repeat (g05kf) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeat (g05kg) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_dist_students_t (g05sn).

References

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

Parameters

Compulsory Input Parameters

1: $n$ – int64int32nag_int scalar: $n$ , the number of pseudorandom numbers to be generated.

Constraint: $n \geq 0$ .
2: $df$ – int64int32nag_int scalar: $ν$ , the number of degrees of freedom of the distribution.

Constraint: $df \geq 1$ .
3: $state (:)$ – int64int32nag_int array: Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).

Contains information on the selected base generator and its current state.

Optional Input Parameters

None.

Output Parameters

1: $state (:)$ – int64int32nag_int array: Contains updated information on the state of the generator.
2: $x (n)$ – double array: The $n$ pseudorandom numbers from the specified Student's $t$ -distribution.
3: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$: Constraint: $n \geq 0$ .

$ifail = 2$: Constraint: $df \geq 1$ .

$ifail = 3$: On entry, state vector has been corrupted or not initialized.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

The time taken by nag_rand_dist_students_t (g05sn) increases with

ν

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_dist_students_t (g05sn), after initialization by nag_rand_init_repeat (g05kf).

Open in the MATLAB editor: g05sn_example

function g05sn_example


fprintf('g05sn example results\n\n');

% Initialize the base generator to a repeatable sequence
seed  = [int64(1762543)];
genid = int64(1);
subid = int64(1);
[state, ifail] = g05kf( ...
                        genid, subid, seed);

% Number of variates
n = int64(5);

% Parameters
df = int64(5);

% Generate variates from a Student t distribution
[state, x, ifail] = g05sn( ...
                           n, df, state);

disp('Variates');
disp(x);

g05sn example results

Variates
    0.3849
   -0.9461
   -2.2814
    0.1127
    0.5272

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox