Logarithm of Cumulative Distribution Function

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

Installation

npm install @stdlib/stats-base-dists-normal-logcdf

Alternatively,

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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 );
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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License

See LICENSE.

Copyright

Copyright © 2016-2022. The Stdlib Authors.

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