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NAG Toolbox

NAG Toolbox: nag_rand_dist_logistic (g05sl)

 Contents

    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example

Purpose

nag_rand_dist_logistic (g05sl) generates a vector of pseudorandom numbers from a logistic distribution with mean a and spread b.

Syntax

[state, x, ifail] = g05sl(n, a, b, state)
[state, x, ifail] = nag_rand_dist_logistic(n, a, b, state)

Description

The distribution has PDF (probability density function)
fx=ex-a/bb 1+ex-a/b 2 .  
nag_rand_dist_logistic (g05sl) returns the value
a+b lny1-y ,  
where y is a pseudorandom number uniformly distributed over 0,1.
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_logistic (g05sl).

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: n0.
2:     a – double scalar
a, the mean of the distribution.
3:     b – double scalar
b, the spread of the distribution, where ‘spread’ is 3π ×standard deviation.
Constraint: b0.0.
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:     xn – double array
The n pseudorandom numbers from the specified logistic 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=3
Constraint: b0.0.
   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 logistic distribution with mean 1.0 and spread 2.0, generated by a single call to nag_rand_dist_logistic (g05sl), after initialization by nag_rand_init_repeat (g05kf).
function g05sl_example


fprintf('g05sl 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
a = 1;
b = 2;

% Generate variates from a logistic distribution
[state, x, ifail] = g05sl( ...
                           n, a, b, state);

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


g05sl example results

Variates
    2.1193
   -3.2544
    3.1552
    3.7510
   -3.2944


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Chapter Introduction
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