Logarithm of Probability Mass Function

Evaluate the natural logarithm of the probability mass function (PMF) for a discrete uniform distribution.

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

logpmf( x, a, b )

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

var y = logpmf( 2.0, 0, 4 );
// returns ~-1.609

y = logpmf( 5.0, 0, 4 );
// returns -Infinity

y = logpmf( 3, -4, 4 );
// returns ~-2.197

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

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

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

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

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

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

If provided a > b, the function returns NaN.

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

logpmf.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 myLogPMF = logpmf.factory( 6, 7 );
var y = myLogPMF( 7.0 );
// returns ~-0.693

y = myLogPMF( 5.0 );
// returns -Infinity

Examples

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

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 = logpmf( x, a, b );
    console.log( 'x: %d, a: %d, b: %d, ln(P(X=x;a,b)): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}