npm package: @stdlib/stats-base-dists-exponential-ctor
Description: Exponential distribution constructor.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Exponential

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> Exponential distribution constructor.

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<section class="intro">

</section>

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<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-exponential-ctor
```

</section>

<section class="usage">

## Usage

```javascript
var Exponential = require( '@stdlib/stats-base-dists-exponential-ctor' );
```

#### Exponential( \[lambda] )

Returns an [exponential][exponential-distribution] distribution object.

```javascript
var exponential = new Exponential();

var mu = exponential.mean;
// returns 1.0
```

By default, `lambda = 1.0`. To create a distribution having a different rate parameter `lambda`, provide a parameter value.

```javascript
var exponential = new Exponential( 4.0 );

var mu = exponential.mean;
// returns 0.25
```

* * *

## exponential

An [exponential][exponential-distribution] distribution object has the following properties and methods...

### Writable Properties

#### exponential.lambda

Rate parameter of the distribution. `lambda` **must** be a positive number.

```javascript
var exponential = new Exponential( 2.0 );

var lambda = exponential.lambda;
// returns 2.0

exponential.lambda = 3.0;

lambda = exponential.lambda;
// returns 3.0
```

* * *

### Computed Properties

#### Exponential.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var exponential = new Exponential( 4.0 );

var entropy = exponential.entropy;
// returns ~-0.386
```

#### Exponential.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var exponential = new Exponential( 4.0 );

var kurtosis = exponential.kurtosis;
// returns 6.0
```

#### Exponential.prototype.mean

Returns the [expected value][expected-value].

```javascript
var exponential = new Exponential( 4.0 );

var mu = exponential.mean;
// returns 0.25
```

#### Exponential.prototype.median

Returns the [median][median].

```javascript
var exponential = new Exponential( 4.0 );

var median = exponential.median;
// returns ~0.173
```

#### Exponential.prototype.mode

Returns the [mode][mode].

```javascript
var exponential = new Exponential( 4.0 );

var mode = exponential.mode;
// returns 0.0
```

#### Exponential.prototype.skewness

Returns the [skewness][skewness].

```javascript
var exponential = new Exponential( 4.0 );

var skewness = exponential.skewness;
// returns 2.0
```

#### Exponential.prototype.stdev

Returns the [standard deviation][standard-deviation].

```javascript
var exponential = new Exponential( 4.0 );

var s = exponential.stdev;
// returns 0.25
```

#### Exponential.prototype.variance

Returns the [variance][variance].

```javascript
var exponential = new Exponential( 4.0 );

var s2 = exponential.variance;
// returns ~0.063
```

* * *

### Methods

#### Exponential.prototype.cdf( x )

Evaluates the [cumulative distribution function][cdf] (CDF).

```javascript
var exponential = new Exponential( 2.0 );

var y = exponential.cdf( 0.5 );
// returns ~0.632
```

#### Exponential.prototype.logcdf( x )

Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF).

```javascript
var exponential = new Exponential( 2.0 );

var y = exponential.logcdf( 0.5 );
// returns ~-0.459
```

#### Exponential.prototype.logpdf( x )

Evaluates the natural logarithm of the [probability density function][pdf] (PDF).

```javascript
var exponential = new Exponential( 2.0 );

var y = exponential.logpdf( 0.8 );
// returns ~-0.907
```

#### Exponential.prototype.mgf( t )

Evaluates the [moment-generating function][mgf] (MGF).

```javascript
var exponential = new Exponential( 2.0 );

var y = exponential.mgf( 0.5 );
// returns ~1.333
```

#### Exponential.prototype.pdf( x )

Evaluates the [probability density function][pdf] (PDF).

```javascript
var exponential = new Exponential( 2.0 );

var y = exponential.pdf( 0.8 );
// returns ~0.404
```

#### Exponential.prototype.quantile( p )

Evaluates the [quantile function][quantile-function] at probability `p`.

```javascript
var exponential = new Exponential( 2.0 );

var y = exponential.quantile( 0.5 );
// returns ~0.347

y = exponential.quantile( 1.9 );
// returns NaN
```

</section>

<!-- /.usage -->

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<section class="notes">

</section>

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<!-- Package usage examples. -->

* * *

<section class="examples">

## Examples

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

```javascript
var Exponential = require( '@stdlib/stats-base-dists-exponential-ctor' );

var exponential = new Exponential( 2.0 );

var mu = exponential.mean;
// returns 0.5

var mode = exponential.mode;
// returns 0.0

var s2 = exponential.variance;
// returns 0.25

var y = exponential.cdf( 0.8 );
// returns ~0.798
```

</section>

<!-- /.examples -->

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* * *

## 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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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-exponential-ctor/main/LICENSE

[exponential-distribution]: https://en.wikipedia.org/wiki/Exponential_distribution

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

[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function

[pdf]: https://en.wikipedia.org/wiki/Probability_density_function

[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function

[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29

[expected-value]: https://en.wikipedia.org/wiki/Expected_value

[kurtosis]: https://en.wikipedia.org/wiki/Kurtosis

[median]: https://en.wikipedia.org/wiki/Median

[mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29

[skewness]: https://en.wikipedia.org/wiki/Skewness

[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation

[variance]: https://en.wikipedia.org/wiki/Variance

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