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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_rand_dist_students_t (g05sn)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


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


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


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).


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


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


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:
Constraint: n0.
Constraint: df1.
On entry, state vector has been corrupted or not initialized.
An unexpected error has been triggered by this routine. Please contact NAG.
Your licence key may have expired or may not have been installed correctly.
Dynamic memory allocation failed.


Not applicable.

Further Comments

The time taken by nag_rand_dist_students_t (g05sn) increases with ν.


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);


g05sn example results


PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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