Logarithm of Cumulative Distribution Function

Degenerate distribution logarithm of cumulative distribution function.

The cumulative distribution function for a degenerate random variable is

where µ is the constant value of the distribution.

Usage

var logcdf = require( '@stdlib/stats/base/dists/degenerate/logcdf' );

logcdf( x, mu )

Evaluates the natural logarithm of the CDF of a degenerate distribution centered at mu.

var y = logcdf( 2.0, 8.0 );
// returns -Infinity

y = logcdf( 8.0, 8.0 );
// returns 0.0

y = logcdf( 10.0, 8.0 );
// returns 0.0

logcdf.factory( mu )

Returns a function for evaluating the natural logarithm of the cumulative distribution function of a degenerate distribution centered at mu.

var mylogcdf = logcdf.factory( 10.0 );

var y = mylogcdf( 10.0 );
// returns 0.0

y = mylogcdf( 8.0 );
// returns -Infinity

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var logcdf = require( '@stdlib/stats/base/dists/degenerate/logcdf' );

var mu;
var x;
var y;
var i;

for ( i = 0; i < 100; i++ ) {
    x = round( randu()*10.0 );
    mu = round( randu()*10.0 );
    y = logcdf( x, mu );
    console.log( 'x: %d, µ: %d, ln(F(x;µ)): %d', x, mu, y );
}