Probability Mass Function

Discrete uniform distribution probability mass function (PMF).

The probability mass function (PMF) for a discrete uniform random variable is

upper P left-parenthesis upper X equals x semicolon a comma b right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column StartFraction 1 Over b minus a plus 1 EndFraction 2nd Column for x element-of StartSet a comma ellipsis comma b EndSet 2nd Row 1st Column 0 2nd Column otherwise EndLayout

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

Usage

var pmf = require( '@stdlib/math/base/dists/discrete-uniform/pmf' );

pmf( x, a, b )

Evaluates the probability mass function (PMF) for a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

var y = pmf( 2.0, 0, 4 );
// returns ~0.2

y = pmf( 5.0, 0, 4 );
// returns 0.0

y = pmf( 3, -4, 4 );
// returns ~0.111

If provided NaN as any argument, the function returns NaN.

var y = pmf( NaN, -2, 2 );
// returns NaN

y = pmf( 1.0, NaN, 4 );
// returns NaN

y = pmf( 2.0, 0, NaN );
// returns NaN

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

var y = pmf( 2.0, 1, 5.5 );
// returns NaN

If provided a > b, the function returns NaN.

var y = pmf( 2.0, 3, 2 );
// returns NaN

pmf.factory( a, b )

Returns a function for evaluating the PMF for a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

var myPDF = pmf.factory( 6, 7 );
var y = myPDF( 7.0 );
// returns 0.5

y = myPDF( 5.0 );
// returns 0.0

Examples

var randint = require( '@stdlib/random/base/discrete-uniform' );
var pmf = require( '@stdlib/math/base/dists/discrete-uniform/pmf' );

var randa = randint.factory( 0, 10 );
var randb = randint.factory();
var a;
var b;
var x;
var y;
var i;

for ( i = 0; i < 25; i++ ) {
    a = randa();
    x = randb( a, a+randa() );
    b = randb( a, a+randa() );
    y = pmf( x, a, b );
    console.log( 'x: %d, a: %d, b: %d, P(X=x;a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}