# Logarithm of Cumulative Distribution Function

Evaluate the natural logarithm of the cumulative distribution function for an exponential distribution.

The cumulative distribution function for an exponential random variable is

where λ is the rate parameter.

## Usage

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


#### logcdf( x, lambda )

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

var y = logcdf( 2.0, 0.3 );
// returns ~-0.796

y = logcdf( 10.0, 0.3 );
// returns ~-0.051


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

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

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


If provided lambda < 0, the function returns NaN.

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


#### logcdf.factory( lambda )

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

var mylogcdf = logcdf.factory( 0.1 );

var y = mylogcdf( 8.0 );
// returns ~-0.597

y = mylogcdf( 2.0 );
// returns ~-1.708

y = mylogcdf( 0.0 );
// returns -Infinity


## Examples

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

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

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