g05tf generates a vector of pseudorandom integers from the discrete logarithmic distribution with parameter

a

Syntax

C#
public static void g05tf( int mode, int n, double a, double[] r, G05..::..G05State g05state, int[] x, out int ifail )

Visual Basic
Public Shared Sub g05tf ( _ mode As Integer, _ n As Integer, _ a As Double, _ r As Double(), _ g05state As G05..::..G05State, _ x As Integer(), _ <OutAttribute> ByRef ifail As Integer _ )

Visual C++
public: static void g05tf( int mode, int n, double a, array<double>^ r, G05..::..G05State^ g05state, array<int>^ x, [OutAttribute] int% ifail )

F#
static member g05tf : mode : int * n : int * a : float * r : float[] * g05state : G05..::..G05State * x : int[] * ifail : int byref -> unit

Parameters

mode

Type: System..::..Int32

On entry: a code for selecting the operation to be performed by the method.

$mode = 0$: Set up reference vector only.
$mode = 1$: Generate variates using reference vector set up in a prior call to g05tf.
$mode = 2$: Set up reference vector and generate variates.
$mode = 3$: Generate variates without using the reference vector.

Constraint:

mode = 0

1

2

3

n: Type: System..::..Int32
On entry: $n$ , the number of pseudorandom numbers to be generated.

Constraint: $n \geq 0$ .

a: Type: System..::..Double
On entry: $a$ , the parameter of the logarithmic distribution.

Constraint: $0.0 < a < 1.0$ .

r: Type: array<System..::..Double>[]()[][]
An array of size [lr]
On entry: if $mode = 1$ , the reference vector from the previous call to g05tf.
If $mode = 3$ , r is not referenced.

On exit: $mode \neq 3$ , the reference vector.

g05state: Type: NagLibrary..::..G05..::..G05State
An Object of type G05.G05State.

x: Type: array<System..::..Int32>[]()[][]
An array of size [n]
On exit: the $n$ pseudorandom numbers from the specified logarithmic distribution.

ifail: Type: System..::..Int32%
On exit: $ifail = 0$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

Description

g05tf generates

n

integers

x_{i}

from a discrete logarithmic distribution, where the probability of

x_{i} = I

P (x_{i} = I) = - \frac{a^{I}}{I \times \log (1 - a)}, I = 1, 2, \dots,

where

0 < a < 1 .

The variates can be generated with or without using a search table and index. If a search table is used then it is stored with the index in a reference vector and subsequent calls to g05tf with the same parameter value can then use this reference vector to generate further variates.

One of the initialization methods (G05KFF not in this release) (for a repeatable sequence if computed sequentially) or (G05KGF not in this release) (for a non-repeatable sequence) must be called prior to the first call to g05tf.

References

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

Error Indicators and Warnings

Errors or warnings detected by the method:

$ifail = 1$: On entry, $mode \neq 0$ , $1$ , $2$ or $3$ .

$ifail = 2$: On entry, $n < 0$ .

$ifail = 3$

On entry,	$a \leq 0.0$ ,
or	$a \geq 1.0$ .

$ifail = 4$: On entry, a is not the same as when r was set up in a previous call to g05tf with $mode = 0$ or $2$ .
On entry, the r vector was not initialized correctly, or has been corrupted.