One of the initialization functions nag_rand_init_repeat (g05kf) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeat (g05kg) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_dist_expmix (g05sg).

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

Parameters

Compulsory Input Parameters

1: $n$ – int64int32nag_int scalar

n

, the number of pseudorandom numbers to be generated.

Constraint:

n \geq 0

2: $a (nmix)$ – double array

The

m

parameters

a_{i}

for the

m

exponential distributions in the mix.

Constraint:

a (i) > 0.0

, for

i = 1, 2, \dots, nmix

3: $wgt (nmix)$ – double array

The

m

weights

w_{i}

for the

m

exponential distributions in the mix.

Constraints:

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

4: $state (:)$ – int64int32nag_int array

Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).

Contains information on the selected base generator and its current state.

Optional Input Parameters

1: $nmix$ – int64int32nag_int scalar: Default: the dimension of the arrays a, wgt. (An error is raised if these dimensions are not equal.)
$m$ , the number of exponential distributions in the mix.

Constraint: $nmix \geq 1$ .

Output Parameters

1: $state (:)$ – int64int32nag_int array: Contains updated information on the state of the generator.
2: $x (n)$ – double array: The $n$ pseudorandom numbers from the specified exponential mix distribution.
3: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$: Constraint: $n \geq 0$ .

$ifail = 2$: Constraint: $nmix \geq 1$ .

$ifail = 3$: Constraint: $a (i) > 0.0$ .

$ifail = 4$: Constraint: sum of $wgt = 1.0$ .

Constraint: $wgt (i) \geq 0.0$ .

$ifail = 5$: On entry, state vector has been corrupted or not initialized.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

None.

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_dist_expmix (g05sg), after initialization by nag_rand_init_repeat (g05kf).

Open in the MATLAB editor: g05sg_example

function g05sg_example


fprintf('g05sg example results\n\n');

% Initialize the base generator to a repeatable sequence
seed  = [int64(1762543)];
genid = int64(1);
subid = int64(1);
[state, ifail] = g05kf( ...
                        genid, subid, seed);

% Number of variates
n = int64(5);

% Parameters
a   = [1;   5;   2];
wgt = [0.5; 0.3; 0.2];

% Generate variates from an exponential mix distribution
[state, x, ifail] = g05sg( ...
                           n, a, wgt, state);

disp('Variates');
disp(x);

g05sg example results

Variates
    0.4520
    2.2398
    1.4649
    0.2253
   11.2884

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox