Cumulative Distribution Function

Exponential distribution cumulative distribution function.

The cumulative distribution function for an exponential random variable is

upper F left-parenthesis x semicolon lamda right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 1 minus 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 cdf = require( '@stdlib/math/base/dists/exponential/cdf' );

cdf( x, lambda )

Evaluates the cumulative distribution function for an exponential distribution with rate parameter lambda.

var y = cdf( 2.0, 0.3 );
// returns ~0.451

y = cdf( 10.0, 0.3 );
// returns ~0.95

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

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

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

If provided lambda < 0, the function returns NaN.

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

cdf.factory( lambda )

Returns a function for evaluating the cumulative distribution function (CDF) for an exponential distribution with rate parameter lambda.

var mycdf = cdf.factory( 0.1 );

var y = mycdf( 8.0 );
// returns ~0.551

y = mycdf( 2.0 );
// returns ~0.181

y = mycdf( 0.0 );
// returns 0.0

Examples

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

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

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