Moment-Generating Function

Discrete uniform distribution moment-generating function (MGF).

The moment-generating function for a discrete uniform random variable is

where a is the minimum support and b is the maximum support. The parameters must satisfy a <= b.

Usage

var mgf = require( '@stdlib/stats/base/dists/discrete-uniform/mgf' );

mgf( t, a, b )

Evaluates the moment-generating function (MGF) for a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

var y = mgf( 2.0, 0, 4 );
// returns ~689.475

y = mgf( -0.2, 0, 4 );
// returns ~0.697

y = mgf( 2.0, 0, 1 );
// returns ~4.195

If a or b is not an integer value, the function returns NaN.

var y = mgf( 0.2, 1, 5.5 );
// returns NaN

If provided a > b, the function returns NaN.

var y = mgf( 0.5, 3, 2);
// returns NaN

If provided NaN for any parameter, the function returns NaN.

var y = mgf( NaN, 0, 1 );
// returns NaN

y = mgf( 0.0, NaN, 1 );
// returns NaN

y = mgf( 0.0, 0, NaN );
// returns NaN

mgf.factory( a, b )

Returns a function for evaluating the moment-generating function (MGF) of a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

var mymgf = mgf.factory( 6, 7 );
var y = mymgf( 0.1 );
// returns ~1.918

y = mymgf( 1.1 );
// returns ~1471.722

Examples

var randint = require( '@stdlib/random/base/discrete-uniform' );
var randu = require( '@stdlib/random/base/randu' );
var mgf = require( '@stdlib/stats/base/dists/discrete-uniform/mgf' );

var randa = randint.factory( 0, 5 );
var randb = randint.factory();
var a;
var b;
var t;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    t = randu();
    a = randa();
    b = randb( a, a+randa() );
    v = mgf( t, a, b );
    console.log( 't: %d, a: %d, b: %d, M_X(t;a,b): %d', t.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}

C APIs

Usage

#include "stdlib/stats/base/dists/discrete-uniform/mgf.h"

stdlib_base_dists_discrete_uniform_mgf( t, a, b )

Evaluates the moment-generating function (MGF) for a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

double out = stdlib_base_dists_discrete_uniform_mgf( 2.0, 0, 4 );
// returns ~689.475

The function accepts the following arguments:

t: [in] double input value.
a: [in] int32_t minimum support.
b: [in] int32_t maximum support.

double stdlib_base_dists_discrete_uniform_mgf( const double t, const int32_t a, const int32_t b );

Examples

#include "stdlib/stats/base/dists/discrete-uniform/mgf.h"
#include "stdlib/math/base/special/round.h"
#include <stdint.h>
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    int32_t a;
    int32_t b;
    double t;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        t = random_uniform( -10.0, 10.0 );
        a = stdlib_base_round( random_uniform( 0.0, 10.0 ) );
        b = stdlib_base_round( random_uniform( 0.0, 10.0 ) ) + a;
        y = stdlib_base_dists_discrete_uniform_mgf( t, a, b );
        printf( "t: %lf, a: %d, b: %d, M_X(t;a,b): %lf\n", t, a, b, y );
    }
}