Logarithm of Probability Density Function

Evaluate the natural logarithm of the probability density function (PDF) for an Erlang distribution.

The probability density function (PDF) for an Erlang random variable is

where k is the shape parameter and lambda is the rate parameter.

Usage

var logpdf = require( '@stdlib/stats/base/dists/erlang/logpdf' );

logpdf( x, k, lambda )

Evaluates the natural logarithm of the probability density function (PDF) for an Erlang distribution with parameters k (shape parameter) and lambda (rate parameter).

var y = logpdf( 0.1, 1, 1.0 );
// returns ~-0.1

y = logpdf( 0.5, 2, 2.5 );
// returns ~-0.111

y = logpdf( -1.0, 4, 2.0 );
// returns -Infinity

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

var y = logpdf( NaN, 1, 1.0 );
// returns NaN

y = logpdf( 0.0, NaN, 1.0 );
// returns NaN

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

If not provided a nonnegative integer for k, the function returns NaN.

var y = logpdf( 2.0, -2, 0.5 );
// returns NaN

y = logpdf( 2.0, 0.5, 0.5 );
// returns NaN

If provided k = 0, the function evaluates the logarithm of the PDF of a degenerate distribution centered at 0.

var y = logpdf( 2.0, 0.0, 2.0 );
// returns -Infinity

y = logpdf( 0.0, 0.0, 2.0 );
// returns Infinity

If provided lambda <= 0, the function returns NaN.

var y = logpdf( 2.0, 1, 0.0 );
// returns NaN

y = logpdf( 2.0, 1, -1.0 );
// returns NaN

logpdf.factory( k, lambda )

Returns a function for evaluating the PDF for an Erlang distribution with parameters k (shape parameter) and lambda (rate parameter).

var mylogpdf = logpdf.factory( 3, 1.5 );

var y = mylogpdf( 1.0 );
// returns ~-0.977

y = mylogpdf( 4.0 );
// returns ~-2.704

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var logpdf = require( '@stdlib/stats/base/dists/erlang/logpdf' );

var lambda;
var k;
var x;
var y;
var i;

for ( i = 0; i < 20; i++ ) {
    x = randu() * 10.0;
    k = round( randu() * 10.0 );
    lambda = randu() * 5.0;
    y = logpdf( x, k, lambda );
    console.log( 'x: %d, k: %d, λ: %d, ln(f(x;k,λ)): %d', x.toFixed( 4 ), k, lambda.toFixed( 4 ), y.toFixed( 4 ) );
}