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_logistic (g05sl)

Purpose

nag_rand_dist_logistic (g05sl) generates a vector of pseudorandom numbers from a logistic distribution with mean aa and spread bb.

Syntax

[state, x, ifail] = g05sl(n, a, b, state)
[state, x, ifail] = nag_rand_dist_logistic(n, a, b, state)

Description

The distribution has PDF (probability density function)
f(x) = (e(xa) / b)/(b (1 + e(xa) / b)2).
f(x)=e(x-a)/bb (1+e(x-a)/b) 2 .
nag_rand_dist_logistic (g05sl) returns the value
a + b ln(y/(1y)) ,
a+b ln(y1-y ) ,
where yy is a pseudorandom number uniformly distributed over (0,1)(0,1).
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_logistic (g05sl).

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:     a – double scalar
aa, the mean of the distribution.
3:     b – double scalar
bb, the spread of the distribution, where ‘spread’ is (sqrt(3))/π × 3π ×standard deviation.
Constraint: b0.0b0.0.
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 logistic 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 = 3ifail=3
On entry, b < 0.0b<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_logistic_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
a = 1;
b = 2;
% Initialize the generator to a repeatable sequence
[state, ifail] = nag_rand_init_repeat(genid, subid, seed);
[state, x, ifail] = nag_rand_dist_logistic(n, a, b, state)
 

state =

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


x =

    2.1193
   -3.2544
    3.1552
    3.7510
   -3.2944


ifail =

                    0


function g05sl_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
a = 1;
b = 2;
% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf(genid, subid, seed);
[state, x, ifail] = g05sl(n, a, b, state)
 

state =

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


x =

    2.1193
   -3.2544
    3.1552
    3.7510
   -3.2944


ifail =

                    0



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

© The Numerical Algorithms Group Ltd, Oxford, UK. 2009–2013