npm package: @stdlib/stats-base-dists-lognormal-cdf
Description: Lognormal distribution cumulative distribution function (CDF).
Author: The Stdlib Authors
Latest version: 0.2.3

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# Cumulative Distribution Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> [Lognormal][lognormal-distribution] distribution [cumulative distribution function][cdf].

<section class="intro">

The [cumulative distribution function][cdf] for a [lognormal][lognormal-distribution] random variable is

<!-- <equation class="equation" label="eq:cdf" align="center" raw="F(x;\mu,\sigma)=\frac12 + \frac12\,\operatorname{erf}\left[\frac{\ln x-\mu}{\sqrt{2}\sigma}\right]" alt="Cumulative distribution function for a lognormal distribution."> -->

<div class="equation" align="center" data-raw-text="F(x;\mu,\sigma)=\frac12 + \frac12\,\operatorname{erf}\left[\frac{\ln x-\mu}{\sqrt{2}\sigma}\right]" data-equation="eq:cdf">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/lognormal/cdf/docs/img/equation_cdf.svg" alt="Cumulative distribution function for a lognormal distribution.">
    <br>
</div>

<!-- </equation> -->

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][lognormal-distribution] follows a [normal distribution][normal-distribution].

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### cdf( x, mu, sigma )

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

```javascript
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`.

```javascript
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`.

```javascript
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][cdf] of a [lognormal][lognormal-distribution] distribution with parameters `mu` (location parameter) and `sigma` (scale parameter).

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

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

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

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdf = require( '@stdlib/stats-base-dists-lognormal-cdf' );

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

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

</section>

<!-- /.examples -->

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<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function

[lognormal-distribution]: https://en.wikipedia.org/wiki/Lognormal_distribution

[normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution

</section>

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