g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rand_logistic (g05slc)

## 1  Purpose

nag_rand_logistic (g05slc) generates a vector of pseudorandom numbers from a logistic distribution with mean $a$ and spread $b$.

## 2  Specification

 #include #include
 void nag_rand_logistic (Integer n, double a, double b, Integer state[], double x[], NagError *fail)

## 3  Description

The distribution has PDF (probability density function)
 $fx=ex-a/bb 1+ex-a/b 2 .$
nag_rand_logistic (g05slc) returns the value
 $a+b lny1-y ,$
where $y$ is a pseudorandom number uniformly distributed over $\left(0,1\right)$.
One of the initialization functions nag_rand_init_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_logistic (g05slc).

## 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

1:     nIntegerInput
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
On entry: $a$, the mean of the distribution.
3:     bdoubleInput
On entry: $b$, the spread of the distribution, where ‘spread’ is $\frac{\sqrt{3}}{\pi }×\text{}$standard deviation.
Constraint: ${\mathbf{b}}\ge 0.0$.
4:     state[$\mathit{dim}$]IntegerCommunication Array
Note: the actual argument supplied must be the array state supplied to the initialization functions nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
5:     x[n]doubleOutput
On exit: the $n$ pseudorandom numbers from the specified logistic distribution.
6:     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_INVALID_STATE
On entry, state vector has been corrupted or not initialized.
NE_REAL
On entry, ${\mathbf{b}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{b}}\ge 0.0$.

Not applicable.

None.

## 9  Example

This example prints the first five pseudorandom real numbers from a logistic distribution with mean $1.0$ and spread $2.0$, generated by a single call to nag_rand_logistic (g05slc), after initialization by nag_rand_init_repeatable (g05kfc).

### 9.1  Program Text

Program Text (g05slce.c)

None.

### 9.3  Program Results

Program Results (g05slce.r)