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

About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Logarithm of Cumulative Distribution Function

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

Installation

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

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 uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var logcdf = require( '@stdlib/stats-base-dists-normal-logcdf' );

var opts = {
    'dtype': 'float64'
};
var sigma = uniform( 10, 0.0, 20.0, opts );
var mu = uniform( 10, -5.0, 5.0, opts );
var x = uniform( 10, 0.0, 10.0, opts );

logEachMap( 'x: %0.4f, µ: %0.4f, σ: %0.4f, ln(F(x;µ,σ)): %0.4f', x, mu, sigma, logcdf );

---

C APIs

Usage

#include "stdlib/stats/base/dists/normal/logcdf.h"

stdlib_base_dists_normal_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).

double out = stdlib_base_dists_normal_cdf( 2.0, 0.0, 1.0 );
// returns ~-0.023

The function accepts the following arguments:

• x: [in] double input value.
• mu: [in] double mean.
• sigma: [in] double standard deviation.

double stdlib_base_dists_normal_logcdf( cconst double x, const double mu, const double sigma );

Examples

#include "stdlib/stats/base/dists/normal/logcdf.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double sigma;
    double mu;
    double x;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        x = random_uniform( 0.0, 10.0 );
        mu = random_uniform( -5.0, 5.0 );
        sigma = random_uniform( 0.1, 20.0 );
        y = stdlib_base_dists_normal_logcdf( x, mu, sigma );
        printf( "x: %lf, µ: %lf, σ: %lf, ln(F(x;µ,σ)): %lf\n", 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.

Community

---

License

See LICENSE.

Copyright

Copyright 2016-2026. The Stdlib Authors.