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# NAG Toolbox: nag_rand_dist_logistic (g05sl)

## 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 $\left(0,1\right)$.
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:     $\mathrm{n}$int64int32nag_int scalar
$n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
2:     $\mathrm{a}$ – double scalar
$a$, the mean of the distribution.
3:     $\mathrm{b}$ – double scalar
$b$, the spread of the distribution, where ‘spread’ is $\frac{\sqrt{3}}{\pi }×\text{}$standard deviation.
Constraint: ${\mathbf{b}}\ge 0.0$.
4:     $\mathrm{state}\left(:\right)$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.

None.

### Output Parameters

1:     $\mathrm{state}\left(:\right)$int64int32nag_int array
Contains updated information on the state of the generator.
2:     $\mathrm{x}\left({\mathbf{n}}\right)$ – double array
The $n$ pseudorandom numbers from the specified logistic distribution.
3:     $\mathrm{ifail}$int64int32nag_int scalar
${\mathbf{ifail}}={\mathbf{0}}$ unless the function detects an error (see Error Indicators and Warnings).

## Error Indicators and Warnings

Errors or warnings detected by the function:
${\mathbf{ifail}}=1$
Constraint: ${\mathbf{n}}\ge 0$.
${\mathbf{ifail}}=3$
Constraint: ${\mathbf{b}}\ge 0.0$.
${\mathbf{ifail}}=4$
On entry, state vector has been corrupted or not initialized.
${\mathbf{ifail}}=-99$
An unexpected error has been triggered by this routine. Please contact NAG.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.

Not applicable.

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

```

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

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