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/stats/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

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 logcdf = require( '@stdlib/stats/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 );
}