g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rand_exp_mix (g05sgc)

## 1  Purpose

nag_rand_exp_mix (g05sgc) generates a vector of pseudorandom numbers from an exponential mix distribution composed of $m$ exponential distributions each having a mean ${a}_{i}$ and weight ${w}_{i}$.

## 2  Specification

 #include #include
 void nag_rand_exp_mix (Integer n, Integer nmix, const double a[], const double wgt[], Integer state[], double x[], NagError *fail)

## 3  Description

The distribution has PDF (probability density function)
 $fx = ∑i=1m 1ai wi e-x/ai if ​x≥0, fx = 0 otherwise,$
where $\sum _{i=1}^{m}{w}_{i}=1$ and ${a}_{i}>0$, ${w}_{i}\ge 0$.
nag_rand_exp_mix (g05sgc) returns the values ${x}_{i}$ by selecting, with probability ${w}_{j}$, random variates from an exponential distribution with argument ${a}_{j}$.
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_exp_mix (g05sgc).

## 4  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

## 5  Arguments

1:     nIntegerInput
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
2:     nmixIntegerInput
On entry: $m$, the number of exponential distributions in the mix.
Constraint: ${\mathbf{nmix}}\ge 1$.
3:     a[nmix]const doubleInput
On entry: the $m$ parameters ${a}_{i}$ for the $m$ exponential distributions in the mix.
Constraint: ${\mathbf{a}}\left[\mathit{i}-1\right]>0.0$, for $\mathit{i}=1,2,\dots ,{\mathbf{nmix}}$.
4:     wgt[nmix]const doubleInput
On entry: the $m$ weights ${w}_{i}$ for the $m$ exponential distributions in the mix.
Constraints:
• $\sum _{\mathit{i}=1}^{m}{\mathbf{wgt}}\left[\mathit{i}-1\right]=1.0$;
• ${\mathbf{wgt}}\left[\mathit{i}-1\right]\ge 0.0$, for $\mathit{i}=1,2,\dots ,m$.
5:     state[$\mathit{dim}$]IntegerCommunication Array
Note: the actual argument supplied must be the array state supplied to the initialization functions 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 exponential mix distribution.
7:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 0$.
On entry, ${\mathbf{nmix}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{nmix}}\ge 1$.
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_ARRAY
On entry, ${\mathbf{a}}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{a}}\left[i-1\right]>0.0$.
On entry, sum of ${\mathbf{wgt}}=〈\mathit{\text{value}}〉$.
Constraint: sum of ${\mathbf{wgt}}=1.0$.
On entry, ${\mathbf{wgt}}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{wgt}}\left[i-1\right]\ge 0.0$.

Not applicable.

None.

## 9  Example

This example prints the first five pseudorandom numbers from an exponential mix distribution comprising three exponential distributions with parameters ${a}_{1}=1.0$, ${a}_{2}=5.0$ and ${a}_{3}=2.0$, and with respective weights $0.5$, $0.3$ and $0.2$. The numbers are generated by a single call to nag_rand_exp_mix (g05sgc), after initialization by nag_rand_init_repeatable (g05kfc).

### 9.1  Program Text

Program Text (g05sgce.c)

None.

### 9.3  Program Results

Program Results (g05sgce.r)