Logarithm of Probability Density Function

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

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

where λ is the rate parameter.

Usage

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

logpdf( x, lambda )

Evaluates the natural logarithm of the probability density function (PDF) for an exponential distribution with rate parameter lambda.

var y = logpdf( 2.0, 0.3 );
// returns ~-1.804

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

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

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

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

If provided lambda < 0, the function returns NaN.

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

logpdf.factory( lambda )

Returns a function for evaluating the natural logarithm of the probability density function (PDF) for an exponential distribution with rate parameter lambda.

var mylogpdf = logpdf.factory( 0.1 );

var y = mylogpdf( 8.0 );
// returns ~-3.103

y = mylogpdf( 5.0 );
// returns ~-2.803

Notes

In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.

Examples

var randu = require( '@stdlib/random/base/randu' );
var logpdf = require( '@stdlib/stats/base/dists/exponential/logpdf' );

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

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    lambda = randu() * 10.0;
    y = logpdf( x, lambda );
    console.log( 'x: %d, λ: %d, ln(f(x;λ)): %d', x, lambda, y );
}