g05sp generates a vector of pseudorandom numbers from a triangular distribution with parameters

x_{\min}

x_{med}

and

x_{\max}

Syntax

C#
public static void g05sp( int n, double xmin, double xmed, double xmax, G05..::..G05State g05state, double[] x, out int ifail )

Visual Basic
Public Shared Sub g05sp ( _ n As Integer, _ xmin As Double, _ xmed As Double, _ xmax As Double, _ g05state As G05..::..G05State, _ x As Double(), _ <OutAttribute> ByRef ifail As Integer _ )

Visual C++
public: static void g05sp( int n, double xmin, double xmed, double xmax, G05..::..G05State^ g05state, array<double>^ x, [OutAttribute] int% ifail )

F#
static member g05sp : n : int * xmin : float * xmed : float * xmax : 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: $n \geq 0$ .

xmin: Type: System..::..Double
On entry: the end point $x_{\min}$ of the triangular distribution.

xmed: Type: System..::..Double
On entry: the median of the distribution $x_{med}$ (also the location of the vertex of the triangular distribution at which the PDF reaches a maximum).

Constraint: $xmed \geq xmin$ .

xmax: Type: System..::..Double
On entry: the end point $x_{\max}$ of the triangular distribution.

Constraint: $xmax \geq xmed$ .

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 triangular 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 triangular distribution has a PDF (probability density function) that is triangular in profile. The base of the triangle ranges from

x = x_{\min}

x = x_{\max}

and the PDF has a maximum value of

\frac{2}{x_{\max} - x_{\min}}

x = x_{med}

. If

x_{\min} = x_{med} = x_{\max}

then

x = x_{med}

with probability 1; otherwise the triangular distribution has PDF:

\begin{array}{l} f (x) = \frac{x - x_{\min}}{x_{med} - x_{\min}} \times \frac{2}{x_{\max} - x_{\min}} & ​ if ​ x_{\min} \leq x \leq x_{med}, \\ f (x) = \frac{x_{\max} - x}{x_{\max} - x_{med}} \times \frac{2}{x_{\max} - x_{\min}} & ​ if ​ x_{med} < x \leq x_{\max}, \\ f (x) = 0 & ​ otherwise. \end{array}

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 g05sp.

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, $n < 0$ .

$ifail = 3$: On entry, $xmed < xmin$ .

$ifail = 4$: On entry, $xmax < xmed$ .

$ifail = 5$

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#): g05spe.cs

Example program data: g05spe.d

Example program results: g05spe.r