Probability Density Function

Exponential distribution probability density function (PDF).

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

f left-parenthesis x semicolon lamda right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column lamda e Superscript minus lamda x Baseline 2nd Column x greater-than-or-equal-to 0 2nd Row 1st Column 0 2nd Column x less-than 0 EndLayout

where λ is the rate parameter.

Usage

var pdf = require( '@stdlib/math/base/dists/exponential/pdf' );

pdf( x, lambda )

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

var y = pdf( 2.0, 0.3 );
// returns ~0.165

y = pdf( 2.0, 1.0 );
// returns ~0.135

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

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

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

If provided lambda < 0, the function returns NaN.

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

pdf.factory( lambda )

Partially apply lambda to create a reusable function for evaluating the PDF.

var mypdf = pdf.factory( 0.1 );

var y = mypdf( 8.0 );
// returns ~0.045

y = mypdf( 5.0 );
// returns ~0.06

Examples

var randu = require( '@stdlib/random/base/randu' );
var pdf = require( '@stdlib/math/base/dists/exponential/pdf' );

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

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