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g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Documentnag_rngs_triangular (g05lhc)

1  Purpose

nag_rngs_triangular (g05lhc) generates a vector of pseudorandom numbers from a triangular distribution with parameters ${x}_{\mathrm{min}}$, ${x}_{\mathrm{max}}$ and ${x}_{\mathrm{med}}$.

2  Specification

 #include #include
 void nag_rngs_triangular (double xmin, double xmax, double xmed, Integer n, double x[], Integer igen, Integer iseed[], NagError *fail)

3  Description

The triangular distribution has a PDF (probability density function) that is triangular in profile. The base of the triangle ranges from $x={x}_{\mathrm{min}}$ to $x={x}_{\mathrm{max}}$ and the PDF has a maximum value of $\frac{2}{{x}_{\mathrm{max}}-{x}_{\mathrm{min}}}$ at $x={x}_{\mathrm{med}}$. If ${x}_{\mathrm{min}}={x}_{\mathrm{med}}={x}_{\mathrm{max}}$ then $x={x}_{\mathrm{med}}$ with probability 1; otherwise the triangular distribution has PDF:
 $fx= x-xmin xmed-xmin ×2xmax-xmin ​ if ​xmin
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_triangular (g05lhc).

4  References

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

5  Arguments

1:     xmindoubleInput
2:     xmaxdoubleInput
On entry: the end points ${x}_{\mathrm{min}}$ and ${x}_{\mathrm{max}}$ of the uniform distribution.
Constraint: ${\mathbf{xmin}}\le {\mathbf{xmax}}$.
3:     xmeddoubleInput
On entry: the median of the distribution ${x}_{\mathrm{med}}$ (also the location of the vertex of the triangular distribution at which the PDF reaches a maximum).
Constraint: ${\mathbf{xmin}}\le {\mathbf{xmed}}\le {\mathbf{xmax}}$.
4:     nIntegerInput
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
5:     x[n]doubleOutput
On exit: the $n$ pseudorandom numbers from the specified triangular distribution.
6:     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).
7:     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.
8:     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_2
On entry, ${\mathbf{xmed}}=〈\mathit{\text{value}}〉$ and ${\mathbf{xmax}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{xmed}}\le {\mathbf{xmax}}$.
On entry, ${\mathbf{xmed}}=〈\mathit{\text{value}}〉$ and ${\mathbf{xmin}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{xmed}}\ge {\mathbf{xmin}}$.
On entry, ${\mathbf{xmin}}=〈\mathit{\text{value}}〉$ and ${\mathbf{xmax}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{xmin}}\le {\mathbf{xmax}}$.

Not applicable.

None.

9  Example

This example prints five pseudorandom numbers from a triangular distribution with parameters ${x}_{\mathrm{min}}=-1.0$, ${x}_{\mathrm{max}}=1.0$ and ${x}_{\mathrm{med}}=0.5$, generated by a single call to nag_rngs_triangular (g05lhc), after initialization by nag_rngs_init_repeatable (g05kbc).

9.1  Program Text

Program Text (g05lhce.c)

None.

9.3  Program Results

Program Results (g05lhce.r)