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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_rand_dist_lognormal (g05sm)

Purpose

nag_rand_dist_lognormal (g05sm) generates a vector of pseudorandom numbers from a log-normal distribution with parameters $\mu$ and ${\sigma }^{2}$.

Syntax

[state, x, ifail] = g05sm(n, xmu, var, state)
[state, x, ifail] = nag_rand_dist_lognormal(n, xmu, var, state)

Description

The distribution has PDF (probability density function)
 $fx = 1 xσ⁢2π exp - ln⁡x-μ 2 2σ2 if ​ x>0 , fx=0 otherwise,$
i.e., $\mathrm{ln}x$ is normally distributed with mean $\mu$ and variance ${\sigma }^{2}$. nag_rand_dist_lognormal (g05sm) evaluates $\mathrm{exp}{y}_{i}$, where the ${y}_{i}$ are generated by nag_rand_dist_normal (g05sk) from a Normal distribution with mean $\mu$ and variance ${\sigma }^{2}$, for $\mathit{i}=1,2,\dots ,n$.
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_lognormal (g05sm).

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:     $\mathrm{xmu}$ – double scalar
$\mu$, the mean of the distribution of $\mathrm{ln}x$.
3:     $\mathrm{var}$ – double scalar
${\sigma }^{2}$, the variance of the distribution of $\mathrm{ln}x$.
Constraint: ${\mathbf{var}}\ge 0.0$.
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 log-normal 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: ${\mathbf{n}}\ge 0$.
${\mathbf{ifail}}=2$
On entry, xmu is too large to take the exponential of .
${\mathbf{ifail}}=3$
Constraint: ${\mathbf{var}}\ge 0.0$.
${\mathbf{ifail}}=4$
On entry, state vector has been corrupted or not initialized.
${\mathbf{ifail}}=-99$
${\mathbf{ifail}}=-399$
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 five pseudorandom numbers from a log-normal distribution with mean $1.0$ and variance $2.0$, generated by a single call to nag_rand_dist_lognormal (g05sm), after initialization by nag_rand_init_repeat (g05kf).
```function g05sm_example

fprintf('g05sm 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
xmu = 1;
var = 2;

% Generate variates from a Log-Normal distribution
[state, x, ifail] = g05sm( ...
n, xmu, var, state);

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

```
```g05sm example results

Variates
4.4515
0.4670
6.9331
8.8597
0.4603

```