g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rand_lognormal (g05smc)

## 1  Purpose

nag_rand_lognormal (g05smc) generates a vector of pseudorandom numbers from a log-normal distribution with parameters $\mu$ and ${\sigma }^{2}$.

## 2  Specification

 #include #include
 void nag_rand_lognormal (Integer n, double xmu, double var, Integer state[], double x[], NagError *fail)

## 3  Description

The distribution has PDF (probability density function)
 $fx = 1 xσ⁢2π exp - ln⁡x-μ 2 2σ2 if ​ x>0 , fx=0 otherwise,$
i.e., $\mathrm{ln}x$ is normally distributed with mean $\mu$ and variance ${\sigma }^{2}$. nag_rand_lognormal (g05smc) evaluates $\mathrm{exp}{y}_{i}$, where the ${y}_{i}$ are generated by nag_rand_normal (g05skc) with mean $\mu$ and variance ${\sigma }^{2}$, for $\mathit{i}=1,2,\dots ,n$.
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_lognormal (g05smc).

## 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: ${\mathbf{n}}\ge 0$.
2:     xmudoubleInput
On entry: $\mu$, the mean of the distribution of $\mathrm{ln}x$.
3:     vardoubleInput
On entry: ${\sigma }^{2}$, the variance of the distribution of $\mathrm{ln}x$.
Constraint: ${\mathbf{var}}\ge 0.0$.
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 log-normal 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, ${\mathbf{var}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{var}}\ge 0.0$.
On entry, xmu is too large to take the exponential of ${\mathbf{xmu}}=〈\mathit{\text{value}}〉$.

Not applicable.

None.

## 9  Example

This example prints five pseudorandom numbers from a log-normal distribution with mean $1.0$ and variance $2.0$, generated by a single call to nag_rand_lognormal (g05smc), after initialization by nag_rand_init_repeatable (g05kfc).

### 9.1  Program Text

Program Text (g05smce.c)

None.

### 9.3  Program Results

Program Results (g05smce.r)