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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_rand_dist_cauchy (g05sc)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_rand_dist_cauchy (g05sc) generates a vector of pseudorandom numbers from a Cauchy distribution with median a and semi-interquartile range b.


[state, x, ifail] = g05sc(n, xmed, semiqr, state)
[state, x, ifail] = nag_rand_dist_cauchy(n, xmed, semiqr, state)


The distribution has PDF (probability density function)
fx=1πb 1+ x-ab 2 .  
nag_rand_dist_cauchy (g05sc) returns the value
a+b2y1- 1y2,  
where y1 and y2 are a pair of consecutive pseudorandom numbers from a uniform distribution over 0,1, such that
2y1-1 2+y221.  
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).


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


Compulsory Input Parameters

1:     n int64int32nag_int scalar
n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2:     xmed – double scalar
a, the median of the distribution.
3:     semiqr – double scalar
b, the semi-interquartile range of the distribution.
Constraint: semiqr0.0.
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


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 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:
Constraint: n0.
Constraint: semiqr0.0.
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



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).
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);


g05sc example results


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

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