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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_rand_dist_exp (g05sf)

## Purpose

nag_rand_dist_exp (g05sf) generates a vector of pseudorandom numbers from a (negative) exponential distribution with mean $a$.

## Syntax

[state, x, ifail] = g05sf(n, a, state)
[state, x, ifail] = nag_rand_dist_exp(n, a, state)

## Description

The exponential distribution has PDF (probability density function):
 $fx = 1a e -x/a if ​x≥0, fx=0 otherwise.$
nag_rand_dist_exp (g05sf) returns the values
 $xi = -a ln⁡yi$
where ${y}_{i}$ are the next $n$ numbers generated by a uniform $\left(0,1\right]$ generator.
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_exp (g05sf).

## 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.
Constraint: ${\mathbf{a}}>0.0$.
3:     $\mathrm{state}\left(:\right)$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 exponential 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: ${\mathbf{n}}\ge 0$.
${\mathbf{ifail}}=2$
Constraint: ${\mathbf{a}}>0.0$.
${\mathbf{ifail}}=3$
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 an exponential distribution with mean $1.0$, generated by a single call to nag_rand_dist_exp (g05sf), after initialization by nag_rand_init_repeat (g05kf).
```function g05sf_example

fprintf('g05sf 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;

% Generate variates from an exponential distribution
[state, x, ifail] = g05sf( ...
n, a, state);

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

```
```g05sf example results

Variates
0.4520
2.2398
0.2930
0.2253
2.2577

```