g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rngs_weibull (g05lmc)

## 1  Purpose

nag_rngs_weibull (g05lmc) generates a vector of pseudorandom numbers from a two parameter Weibull distribution with shape parameter $a$ and scale parameter $b$.

## 2  Specification

 #include #include
 void nag_rngs_weibull (double a, double b, Integer n, double x[], Integer igen, Integer iseed[], NagError *fail)

## 3  Description

The distribution has PDF (probability density function)
 $fx= abxa-1e-xa/b if ​x>0, fx=0 otherwise.$
nag_rngs_weibull (g05lmc) 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_rngs_init_repeatable (g05kbc) (for a repeatable sequence if computed sequentially) or nag_rngs_init_nonrepeatable (g05kcc) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_weibull (g05lmc).

## 4  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

## 5  Arguments

On entry: $a$, the shape parameter of the distribution.
Constraint: ${\mathbf{a}}>0.0$.
2:     bdoubleInput
On entry: $b$, the scale parameter of the distribution.
Constraint: ${\mathbf{b}}>0.0$.
3:     nIntegerInput
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
4:     x[n]doubleOutput
On exit: the $n$ pseudorandom numbers from the specified Weibull distribution.
5:     igenIntegerInput
On entry: must contain the identification number for the generator to be used to return a pseudorandom number and should remain unchanged following initialization by a prior call to nag_rngs_init_repeatable (g05kbc) or nag_rngs_init_nonrepeatable (g05kcc).
6:     iseed[$4$]IntegerCommunication Array
On entry: contains values which define the current state of the selected generator.
On exit: contains updated values defining the new state of the selected generator.
7:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 0$.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_REAL
On entry, ${\mathbf{a}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{a}}>0.0$.
On entry, ${\mathbf{b}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{b}}>0.0$.

Not applicable.

None.

## 9  Example

This example prints the first five pseudorandom real numbers from a Weibull distribution with shape parameter $1.0$ and scale parameter $2.0$, generated by a single call to nag_rngs_weibull (g05lmc), after initialization by nag_rngs_init_repeatable (g05kbc).

### 9.1  Program Text

Program Text (g05lmce.c)

None.

### 9.3  Program Results

Program Results (g05lmce.r)