# 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/math/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


## Examples

var randu = require( '@stdlib/random/base/randu' );
var logpdf = require( '@stdlib/math/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 );
}