Cumulative Distribution Function

Lognormal distribution cumulative distribution function.

The cumulative distribution function for a lognormal random variable is

where mu is the location parameter and sigma > 0 is the scale parameter. According to the definition, the natural logarithm of a random variable from a lognormal distribution follows a normal distribution.

Installation

npm install @stdlib/stats-base-dists-lognormal-cdf

Usage

var cdf = require( '@stdlib/stats-base-dists-lognormal-cdf' );

cdf( x, mu, sigma )

Evaluates the cumulative distribution function (CDF) for a lognormal distribution with parameters mu (location parameter) and sigma (scale parameter).

var y = cdf( 2.0, 0.0, 1.0 );
// returns ~0.756

y = cdf( 5.0, 10.0, 3.0 );
// returns ~0.003

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

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

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

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

If provided sigma <= 0, the function returns NaN.

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

y = cdf( 2.0, 0.0, 0.0 );
// returns NaN

cdf.factory( mu, sigma )

Returns a function for evaluating the cumulative distribution function of a lognormal distribution with parameters mu (location parameter) and sigma (scale parameter).

var mycdf = cdf.factory( 3.0, 1.5 );

var y = mycdf( 1.0 );
// returns ~0.023

y = mycdf( 4.0 );
// returns ~0.141

Examples

var randu = require( '@stdlib/random-base-randu' );
var cdf = require( '@stdlib/stats-base-dists-lognormal-cdf' );

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 = cdf( x, mu, sigma );
    console.log( 'x: %d, µ: %d, σ: %d, F(x;µ,σ): %d', x.toFixed( 4 ), mu.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
}

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 © 2016-2024. The Stdlib Authors.