g05 Chapter Contents
g05 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_rand_triangular (g05spc)

## 1  Purpose

nag_rand_triangular (g05spc) generates a vector of pseudorandom numbers from a triangular distribution with parameters ${x}_{\mathrm{min}}$, ${x}_{\mathrm{med}}$ and ${x}_{\mathrm{max}}$.

## 2  Specification

 #include #include
 void nag_rand_triangular (Integer n, double xmin, double xmed, double xmax, Integer state[], double x[], 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 × 2 xmax-xmin ​ if ​xmin≤x≤xmed, fx= xmax-x xmax-xmed ×2xmax-xmin ​ if ​xmed
One of the initialization functions nag_rand_init_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_triangular (g05spc).

## 4  References

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

## 5  Arguments

1:     nIntegerInput
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
2:     xmindoubleInput
On entry: the end point ${x}_{\mathrm{min}}$ of the triangular distribution.
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: ${\mathbf{xmed}}\ge {\mathbf{xmin}}$.
4:     xmaxdoubleInput
On entry: the end point ${x}_{\mathrm{max}}$ of the triangular distribution.
Constraint: ${\mathbf{xmax}}\ge {\mathbf{xmed}}$.
5:     state[$\mathit{dim}$]IntegerCommunication Array
Note: the dimension, $\mathit{dim}$, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
6:     x[n]doubleOutput
On exit: the $n$ pseudorandom numbers from the specified triangular distribution.
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_INVALID_STATE
On entry, state vector has been corrupted or not initialized.
NE_REAL_2
On entry, ${\mathbf{xmax}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{xmed}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{xmax}}\ge {\mathbf{xmed}}$.
On entry, ${\mathbf{xmed}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{xmin}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{xmed}}\ge {\mathbf{xmin}}$.

Not applicable.

## 8  Parallelism and Performance

nag_rand_triangular (g05spc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

None.

## 10  Example

This example prints five pseudorandom numbers from a triangular distribution with parameters ${x}_{\mathrm{min}}=-1.0$, ${x}_{\mathrm{med}}=0.5$ and ${x}_{\mathrm{max}}=1.0$, generated by a single call to nag_rand_triangular (g05spc), after initialization by nag_rand_init_repeatable (g05kfc).

### 10.1  Program Text

Program Text (g05spce.c)

None.

### 10.3  Program Results

Program Results (g05spce.r)