NAG Library Function Document

nag_rand_exp_mix (g05sgc)

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: n – IntegerInput

On entry:

n

, the number of pseudorandom numbers to be generated.

Constraint:

n \geq 0

2: nmix – IntegerInput

On entry:

m

, the number of exponential distributions in the mix.

Constraint:

nmix \geq 1

3: a[nmix] – const doubleInput

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 doubleInput

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[ $\dim$ ] – IntegerCommunication 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] – doubleOutput

On exit: the

n

pseudorandom numbers from the specified exponential mix distribution.

7: fail – NagError *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.
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.
NE_INVALID_STATE: On entry, state vector has been corrupted or not initialized.
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

nag_rand_exp_mix (g05sgc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

Please 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