# NAG CL Interfaceg05sgc (dist_​expmix)

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## 1Purpose

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 ${w}_{i}$.

## 2Specification

 #include
 void g05sgc (Integer n, Integer nmix, const double a[], const double wgt[], Integer state[], double x[], NagError *fail)
The function may be called by the names: g05sgc, nag_rand_dist_expmix or nag_rand_exp_mix.

## 3Description

The distribution has PDF (probability density function)
 $f(x) = ∑i=1m 1ai wi e-x/ai if ​x≥0, f(x) = 0 otherwise,$
where $\sum _{i=1}^{m}{w}_{i}=1$ and ${a}_{i}>0$, ${w}_{i}\ge 0$.
g05sgc 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 functions g05kfc (for a repeatable sequence if computed sequentially) or g05kgc (for a non-repeatable sequence) must be called prior to the first call to g05sgc.
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

## 5Arguments

1: $\mathbf{n}$Integer Input
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
2: $\mathbf{nmix}$Integer Input
On entry: $m$, the number of exponential distributions in the mix.
Constraint: ${\mathbf{nmix}}\ge 1$.
3: $\mathbf{a}\left[{\mathbf{nmix}}\right]$const double Input
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: $\mathbf{wgt}\left[{\mathbf{nmix}}\right]$const double Input
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: $\mathbf{state}\left[\mathit{dim}\right]$Integer Communication 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: $\mathbf{x}\left[{\mathbf{n}}\right]$double Output
On exit: the $n$ pseudorandom numbers from the specified exponential mix distribution.
7: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_INVALID_STATE
On entry, state vector has been corrupted or not initialized.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
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.

## 8Parallelism and Performance

g05sgc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

None.

## 10Example

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 g05sgc, after initialization by g05kfc.

### 10.1Program Text

Program Text (g05sgce.c)

None.

### 10.3Program Results

Program Results (g05sgce.r)