# @stdlib/stats-base-dists-lognormal-cdf

0.2.2 • Public • Published

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# 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.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-lognormal-cdf`

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