g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rngs_lognormal (g05lkc)

## 1  Purpose

nag_rngs_lognormal (g05lkc) generates a vector of pseudorandom numbers from a log-normal distribution with parameters $\mu$ and ${\sigma }^{2}$.

## 2  Specification

 #include #include
 void nag_rngs_lognormal (double xmu, double var, Integer n, double x[], Integer igen, Integer iseed[], NagError *fail)

## 3  Description

The distribution has PDF (probability density function)
 $fx= 1xσ⁢2π exp- ln⁡x-μ 22σ2 if ​x>0, fx=0 otherwise,$
i.e., $\mathrm{ln}x$ is normally distributed with mean $\mu$ and variance ${\sigma }^{2}$. nag_rngs_lognormal (g05lkc) evaluates $\mathrm{exp}{y}_{i}$, where the ${y}_{i}$ are generated by nag_rngs_normal (g05lac) from a Normal distribution with mean $\mu$ and variance ${\sigma }^{2}$.
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_lognormal (g05lkc).

## 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:     xmudoubleInput
On entry: $\mu$, the mean of the distribution of $\mathrm{ln}x$.
2:     vardoubleInput
On entry: ${\sigma }^{2}$, the variance of the distribution of $\mathrm{ln}x$.
Constraint: ${\mathbf{var}}\ge 0.0$.
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 log-normal 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, ${\mathbf{var}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{var}}\ge 0.0$.

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_rngs_lognormal (g05lkc), after initialization by nag_rngs_init_repeatable (g05kbc).

### 9.1  Program Text

Program Text (g05lkce.c)

None.

### 9.3  Program Results

Program Results (g05lkce.r)