Logarithm of Cumulative Distribution Function

Evaluate the natural logarithm of the cumulative distribution function (CDF) for a normal distribution.

Usage

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

logcdf( x, mu, sigma )

Evaluates the natural logarithm of the cumulative distribution function (CDF) for a normal distribution with parameters mu (mean) and sigma (standard deviation).

var y = logcdf( 2.0, 0.0, 1.0 );
// returns ~-0.023

y = logcdf( -1.0, 4.0, 2.0 );
// returns ~-5.082

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

var y = logcdf( NaN, 0.0, 1.0 );
// returns NaN

y = logcdf( 0.0, NaN, 1.0 );
// returns NaN

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

If provided sigma < 0, the function returns NaN.

var y = logcdf( 2.0, 0.0, -1.0 );
// returns NaN

If provided sigma = 0, the function evaluates the natural logarithm of the CDF of a degenerate distribution centered at mu.

var y = logcdf( 2.0, 8.0, 0.0 );
// returns -Infinity

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

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

logcdf.factory( mu, sigma )

Returns a function for evaluating the cumulative distribution function (CDF) of a normal distribution with parameters mu (mean) and sigma (standard deviation).

var mylogcdf = logcdf.factory( 10.0, 2.0 );

var y = mylogcdf( 10.0 );
// returns ~-0.693

y = mylogcdf( 5.0 );
// returns ~-5.082

Examples

var randu = require( '@stdlib/random/base/randu' );
var logcdf = require( '@stdlib/stats/base/dists/normal/logcdf' );

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

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    mu = (randu() * 10.0) - 5.0;
    sigma = randu() * 20.0;
    y = logcdf( x, mu, sigma );
    console.log( 'x: %d, µ: %d, σ: %d, ln(F(x;µ,σ)): %d', x, mu, sigma, y );
}