g05sg generates a vector of pseudorandom numbers from an exponential mix distribution composed of

m

exponential distributions each having a mean

a_{i}

and weight

w_{i}

Syntax

C#
public static void g05sg( int n, int nmix, double[] a, double[] wgt, G05..::..G05State g05state, double[] x, out int ifail )

Visual Basic
Public Shared Sub g05sg ( _ n As Integer, _ nmix As Integer, _ a As Double(), _ wgt As Double(), _ g05state As G05..::..G05State, _ x As Double(), _ <OutAttribute> ByRef ifail As Integer _ )

Visual C++
public: static void g05sg( int n, int nmix, array<double>^ a, array<double>^ wgt, G05..::..G05State^ g05state, array<double>^ x, [OutAttribute] int% ifail )

F#
static member g05sg : n : int * nmix : int * a : float[] * wgt : float[] * g05state : G05..::..G05State * x : float[] * ifail : int byref -> unit

Parameters

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

Constraint: $n \geq 0$ .

nmix: Type: System..::..Int32
On entry: $m$ , the number of exponential distributions in the mix.

Constraint: $nmix \geq 1$ .

a: Type: array<System..::..Double>[]()[][]
An array of size [nmix]
On entry: the $m$ parameters $a_{i}$ for the $m$ exponential distributions in the mix.

Constraint: $a [i - 1] > 0.0$ , for $i = 1, 2, \dots, nmix$ .

wgt

Type: array<System..::..Double>[]()[][]

An array of size [nmix]

On entry: the

m

weights

w_{i}

for the

m

exponential distributions in the mix.

Constraints:

$\sum_{i = 1}^{m} wgt [i - 1] = 1.0$ ;
$wgt [i - 1] \geq 0.0$ , for $i = 1, 2, \dots, m$ .

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

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

The distribution has PDF (probability density function)

\begin{array}{l} f (x) = \sum_{i = 1}^{m} \frac{1}{a_{i}} w_{i} e^{- x / a_{i}} & if ​ x \geq 0, \\ f (x) = 0 & otherwise, \end{array}

where

\sum_{i = 1}^{m} w_{i} = 1

and

a_{i} > 0

w_{i} \geq 0

g05sg returns the values

x_{i}

by selecting, with probability

w_{j}

, random variates from an exponential distribution with parameter

a_{j}

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 g05sg.

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

Error Indicators and Warnings

Errors or warnings detected by the method:

$ifail = 1$: On entry, $n < 0$ .

$ifail = 2$: On entry, $nmix \leq 0$ .

$ifail = 3$: On entry, $a [i - 1] \leq 0.0$ for at least one $a [i - 1]$ .

$ifail = 4$: On entry, $wgt [i - 1] < 0.0$ for at least one $wgt [i - 1]$ .
On entry, $\sum_{i = 1}^{nmix} wgt [i - 1] \neq 1.0$ .

$ifail = 5$

On entry,

state vector was not initialized or has been corrupted.

$ifail = -9000$: An error occured, see message report.
$ifail = -8000$: Negative dimension for array $〈value〉$
$ifail = -6000$: Invalid Parameters $〈value〉$

Accuracy

Not applicable.

Parallelism and Performance

None.

Further Comments

None.

Example

Example program (C#): g05sge.cs

Example program data: g05sge.d

Example program results: g05sge.r