hide long namesshow long names
hide short namesshow short names
Integer type:  int32  int64  nag_int  show int32  show int32  show int64  show int64  show nag_int  show nag_int

PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_rand_dist_expmix (g05sg)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_rand_dist_expmix (g05sg) generates a vector of pseudorandom numbers from an exponential mix distribution composed of m exponential distributions each having a mean ai and weight wi.


[state, x, ifail] = g05sg(n, a, wgt, state, 'nmix', nmix)
[state, x, ifail] = nag_rand_dist_expmix(n, a, wgt, state, 'nmix', nmix)


The distribution has PDF (probability density function)
fx = i=1m 1ai wi e-x/ai if ​x0, fx = 0 otherwise,  
where i=1mwi=1 and ai>0, wi0.
nag_rand_dist_expmix (g05sg) returns the values xi by selecting, with probability wj, random variates from an exponential distribution with argument aj.
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).


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


Compulsory Input Parameters

1:     n int64int32nag_int scalar
n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2:     anmix – double array
The m parameters ai for the m exponential distributions in the mix.
Constraint: ai>0.0, for i=1,2,,nmix.
3:     wgtnmix – double array
The m weights wi for the m exponential distributions in the mix.
  • i=1mwgti=1.0;
  • wgti0.0, for i=1,2,,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: nmix1.

Output Parameters

1:     state: int64int32nag_int array
Contains updated information on the state of the generator.
2:     xn – 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:
Constraint: n0.
Constraint: nmix1.
Constraint: ai>0.0.
Constraint: sum of wgt=1.0.
Constraint: wgti0.0.
On entry, state vector has been corrupted or not initialized.
An unexpected error has been triggered by this routine. Please contact NAG.
Your licence key may have expired or may not have been installed correctly.
Dynamic memory allocation failed.


Not applicable.

Further Comments



This example prints the first five pseudorandom numbers from an exponential mix distribution comprising three exponential distributions with parameters a1=1.0, a2=5.0 and a3=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).
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);


g05sg example results


PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

© The Numerical Algorithms Group Ltd, Oxford, UK. 2009–2015