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Logarithm of Probability Density Function
Degenerate distribution logarithm of probability density function (logPDF).
Strictly speaking, as a discrete distribution, a degenerate has no probability density function (PDF). Extending the notion of a PDF, we conceptualize the PDF of a degenerate distribution as an infinitely tall spike centered at mu
. More formally,
where delta
is the Dirac delta function.
Usage
var logpdf = require( '@stdlib/stats/base/dists/degenerate/logpdf' );
logpdf( x, mu )
Evaluates the natural logarithm of the PDF of a degenerate distribution centered at mu
.
var y = logpdf( 2.0, 8.0 );
// returns -Infinity
y = logpdf( 8.0, 8.0 );
// returns Infinity
logpdf.factory( mu )
Returns a function for evaluating the natural logarithm of the PDF of a degenerate distribution centered at mu
.
var mylogpdf = logpdf.factory( 10.0 );
var y = mylogpdf( 10.0 );
// returns Infinity
y = mylogpdf( 5.0 );
// returns -Infinity
y = mylogpdf( 12.0 );
// returns -Infinity
Examples
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var logpdf = require( '@stdlib/stats/base/dists/degenerate/logpdf' );
var mu;
var x;
var y;
var i;
for ( i = 0; i < 100; i++ ) {
x = round( randu()*5.0 );
mu = round( randu()*5.0 );
y = logpdf( x, mu );
console.log( 'x: %d, µ: %d, ln(f(x;µ)): %d', x, mu, y );
}