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NAG Toolbox: nag_rand_dist_students_t (g05sn)

 Contents

    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example

Purpose

nag_rand_dist_students_t (g05sn) generates a vector of pseudorandom numbers taken from a Student's t-distribution with ν degrees of freedom.

Syntax

[state, x, ifail] = g05sn(n, df, state)
[state, x, ifail] = nag_rand_dist_students_t(n, df, state)

Description

The distribution has PDF (probability density function)
fx= ν-12 ! 12ν-1!πν 1+x2ν 12ν+1 .  
nag_rand_dist_students_t (g05sn) calculates the values
yiνzi,   i= 1,,n  
where the yi are generated by nag_rand_dist_normal (g05sk) from a Normal distribution with mean 0 and variance 1.0, and the zi are generated by nag_rand_dist_gamma (g05sj) 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_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: n0.
2:     df int64int32nag_int scalar
ν, the number of degrees of freedom of the distribution.
Constraint: df1 .
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:     xn – 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: n0.
   ifail=2
Constraint: df1.
   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).
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

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