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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$a$ and scale parameter b$b$.

## 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)
 f(x) = a/b xa − 1 e − xa / b if ​x > 0, f(x) = 0 otherwise.
$f(x) = ab x a-1 e- xa / b if ​x>0, f(x)=0 otherwise.$
nag_rand_dist_weibull (g05ss) returns the value (blny)1 / a${\left(-b\mathrm{ln}y\right)}^{1/a}$, where y$y$ is a pseudorandom number from a uniform distribution over (0,1]$\left(0,1\right]$.
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:     n – int64int32nag_int scalar
n$n$, the number of pseudorandom numbers to be generated.
Constraint: n0${\mathbf{n}}\ge 0$.
2:     a – double scalar
a$a$, the shape parameter of the distribution.
Constraint: a > 0.0${\mathbf{a}}>0.0$.
3:     b – double scalar
b$b$, the scale parameter of the distribution.
Constraint: b > 0.0${\mathbf{b}}>0.0$.
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.

None.

None.

### Output Parameters

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

## Error Indicators and Warnings

Errors or warnings detected by the function:
ifail = 1${\mathbf{ifail}}=1$
On entry, n < 0${\mathbf{n}}<0$.
ifail = 2${\mathbf{ifail}}=2$
On entry, a0.0${\mathbf{a}}\le 0.0$.
ifail = 3${\mathbf{ifail}}=3$
On entry, b0.0${\mathbf{b}}\le 0.0$.
ifail = 4${\mathbf{ifail}}=4$
 On entry, state vector was not initialized or has been corrupted.

Not applicable.

None.

## Example

function nag_rand_dist_weibull_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
a = 1;
b = 2;
% Initialize the generator to a repeatable sequence
[state, ifail] = nag_rand_init_repeat(genid, subid, seed);
[state, x, ifail] = nag_rand_dist_weibull(n, a, b, state)

state =

17
1234
1
0
4110
11820
23399
29340
17917
13895
19930
8
0
1234
1
1
1234

x =

0.9039
4.4796
0.5860
0.4506
4.5154

ifail =

0

function g05ss_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
a = 1;
b = 2;
% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf(genid, subid, seed);
[state, x, ifail] = g05ss(n, a, b, state)

state =

17
1234
1
0
4110
11820
23399
29340
17917
13895
19930
8
0
1234
1
1
1234

x =

0.9039
4.4796
0.5860
0.4506
4.5154

ifail =

0