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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_rand_dist_weibull (g05ss)

## Purpose

nag_rand_dist_weibull (g05ss) generates a vector of pseudorandom numbers from a two parameter Weibull distribution with shape parameter $a$ and scale parameter $b$.

## Syntax

[state, x, ifail] = g05ss(n, a, b, state)
[state, x, ifail] = nag_rand_dist_weibull(n, a, b, state)

## Description

The distribution has PDF (probability density function)
 $fx = ab x a-1 e- xa / b if ​x>0, fx=0 otherwise.$
nag_rand_dist_weibull (g05ss) returns the value ${\left(-b\mathrm{ln}y\right)}^{1/a}$, where $y$ is a pseudorandom number from a uniform distribution 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_weibull (g05ss).

## 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 shape parameter of the distribution.
Constraint: ${\mathbf{a}}>0.0$.
3:     $\mathrm{b}$ – double scalar
$b$, the scale parameter of the distribution.
Constraint: ${\mathbf{b}}>0.0$.
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 Weibull 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: ${\mathbf{a}}>0.0$.
${\mathbf{ifail}}=3$
Constraint: ${\mathbf{b}}>0.0$.
${\mathbf{ifail}}=4$
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 the first five pseudorandom numbers from a Weibull distribution with shape parameter $1.0$ and scale parameter $2.0$, generated by a single call to nag_rand_dist_weibull (g05ss), after initialization by nag_rand_init_repeat (g05kf).
```function g05ss_example

fprintf('g05ss 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 Weibull distribution
[state, x, ifail] = g05ss( ...
n, a, b, state);

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

```
```g05ss example results

Variates
0.9039
4.4796
0.5860
0.4506
4.5154

```