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.

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: $n$ – Integer Input

On entry:

n

, the number of pseudorandom numbers to be generated.

Constraint:

n \geq 0

2: $nmix$ – Integer Input

On entry:

m

, the number of exponential distributions in the mix.

Constraint:

nmix \geq 1

3: $a [nmix]$ – const double Input

On entry: the

m

parameters

a_{i}

for the

m

exponential distributions in the mix.

Constraint:

a [i - 1] > 0.0

, for

i = 1, 2, \dots, nmix

4: $wgt [nmix]$ – const double Input

On entry: the

m

weights

w_{i}

for the

m

exponential distributions in the mix.

Constraints:

$\sum_{i = 1}^{m} wgt [i - 1] = 1.0$ ;
$wgt [i - 1] \geq 0.0$ , for $i = 1, 2, \dots, m$ .

5: $state [\dim]$ – Integer Communication Array

Note: the dimension,

\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: $x [n]$ – double Output

On exit: the

n

pseudorandom numbers from the specified exponential mix distribution.

7: $fail$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error 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.
NE_BAD_PARAM: On entry, argument $⟨ value ⟩$ had an illegal value.
NE_INT: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 0$ .

On entry, $nmix = ⟨ value ⟩$ .
Constraint: $nmix \geq 1$ .
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, $a [⟨ value ⟩] = ⟨ value ⟩$ .
Constraint: $a [i - 1] > 0.0$ .

On entry, sum of $wgt = ⟨ value ⟩$ .
Constraint: sum of $wgt = 1.0$ .

On entry, $wgt [⟨ value ⟩] = ⟨ value ⟩$ .
Constraint: $wgt [i - 1] \geq 0.0$ .

7 Accuracy

Not applicable.

8 Parallelism 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.

9 Further Comments

None.

10 Example

This example prints the first five pseudorandom numbers from an exponential mix distribution comprising three exponential distributions with parameters