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NAG Toolbox

NAG Toolbox: nag_rand_dist_lognormal (g05sm)

Purpose

nag_rand_dist_lognormal (g05sm) generates a vector of pseudorandom numbers from a log-normal distribution with parameters μμ and σ2σ2.

Syntax

[state, x, ifail] = g05sm(n, xmu, var, state)
[state, x, ifail] = nag_rand_dist_lognormal(n, xmu, var, state)

Description

The distribution has PDF (probability density function)
f(x) = 1/( xσ×sqrt(2π) ) exp(((lnxμ)2)/(2σ2)) if ​ x > 0 ,
f(x) = 0 otherwise,
f(x) = 1 xσ2π exp( - (lnx-μ) 2 2σ2 ) if ​ x>0 , f(x)=0 otherwise,
i.e., lnxlnx is normally distributed with mean μμ and variance σ2σ2. nag_rand_dist_lognormal (g05sm) evaluates expyiexpyi, where the yiyi are generated by nag_rand_dist_normal (g05sk) from a Normal distribution with mean μμ and variance σ2σ2, for i = 1,2,,ni=1,2,,n.
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_lognormal (g05sm).

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
nn, the number of pseudorandom numbers to be generated.
Constraint: n0n0.
2:     xmu – double scalar
μμ, the mean of the distribution of lnxlnx.
3:     var – double scalar
σ2σ2, the variance of the distribution of lnxlnx.
Constraint: var0.0var0.0.
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

None.

Input Parameters Omitted from the MATLAB Interface

None.

Output Parameters

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

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=1
On entry, n < 0n<0.
  ifail = 2ifail=2
On entry, unable to calculate exp(xmu)exp(xmu) as xmu is too large.
  ifail = 3ifail=3
On entry, var < 0.0var<0.0.
  ifail = 4ifail=4
On entry,state vector was not initialized or has been corrupted.

Accuracy

Not applicable.

Further Comments

None.

Example

function nag_rand_dist_lognormal_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
xmu = 1;
var = 2;
% Initialize the generator to a repeatable sequence
[state, ifail] = nag_rand_init_repeat(genid, subid, seed);
[state, x, ifail] = nag_rand_dist_lognormal(n, xmu, var, state)
 

state =

                   17
                 1234
                    1
                    0
                 4110
                11820
                23399
                29340
                17917
                13895
                19930
                    8
                    0
                 1234
                    1
                    1
                 1234


x =

    4.4515
    0.4670
    6.9331
    8.8597
    0.4603


ifail =

                    0


function g05sm_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
xmu = 1;
var = 2;
% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf(genid, subid, seed);
[state, x, ifail] = g05sm(n, xmu, var, state)
 

state =

                   17
                 1234
                    1
                    0
                 4110
                11820
                23399
                29340
                17917
                13895
                19930
                    8
                    0
                 1234
                    1
                    1
                 1234


x =

    4.4515
    0.4670
    6.9331
    8.8597
    0.4603


ifail =

                    0



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Chapter Introduction
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