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_cauchy (g05sc).

References

Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin

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: $xmed$ – double scalar: $a$ , the median of the distribution.
3: $semiqr$ – double scalar: $b$ , the semi-interquartile range of the distribution.

Constraint: $semiqr \geq 0.0$ .
4: $state (:)$ – 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 Cauchy 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: $n \geq 0$ .

$ifail = 3$: Constraint: $semiqr \geq 0.0$ .

$ifail = 4$: 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

None.

Example

This example prints the first five pseudorandom real numbers from a Cauchy distribution with median

1.0

and semi-interquartile range

2.0

, generated by a single call to nag_rand_dist_cauchy (g05sc), after initialization by nag_rand_init_repeat (g05kf).

Open in the MATLAB editor: g05sc_example

function g05sc_example


fprintf('g05sc 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
xmed = 1;
semiqr = 2;

% Generate variates from Cauchy distribution
[state, x, ifail] = g05sc( ...
                           n, xmed, semiqr, state);

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

g05sc example results

Variates
    6.1229
    2.2328
   -2.2118
    0.4118
    0.9892

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

Chapter Contents

Chapter Introduction

NAG Toolbox