@stdlib/stats/base/dists/exponential/README.md

Standard library statistical functions.

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# Exponential

> Exponential distribution.

<section class="usage">

## Usage

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

#### exponential

Exponential distribution.

```javascript
var dist = exponential;
// returns {...}
```

The namespace contains the following distribution functions:

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<div class="namespace-toc">

-   <span class="signature">[`cdf( x, lambda )`][@stdlib/stats/base/dists/exponential/cdf]</span><span class="delimiter">: </span><span class="description">exponential distribution cumulative distribution function.</span>
-   <span class="signature">[`logcdf( x, lambda )`][@stdlib/stats/base/dists/exponential/logcdf]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of the cumulative distribution function for an exponential distribution.</span>
-   <span class="signature">[`logpdf( x, lambda )`][@stdlib/stats/base/dists/exponential/logpdf]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of the probability density function (PDF) for an exponential distribution.</span>
-   <span class="signature">[`mgf( t, lambda )`][@stdlib/stats/base/dists/exponential/mgf]</span><span class="delimiter">: </span><span class="description">exponential distribution moment-generating function (MGF).</span>
-   <span class="signature">[`pdf( x, lambda )`][@stdlib/stats/base/dists/exponential/pdf]</span><span class="delimiter">: </span><span class="description">exponential distribution probability density function (PDF).</span>
-   <span class="signature">[`quantile( p, lambda )`][@stdlib/stats/base/dists/exponential/quantile]</span><span class="delimiter">: </span><span class="description">exponential distribution quantile function.</span>

</div>

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The namespace contains the following functions for calculating distribution properties:

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<div class="namespace-toc">

-   <span class="signature">[`entropy( lambda )`][@stdlib/stats/base/dists/exponential/entropy]</span><span class="delimiter">: </span><span class="description">exponential distribution differential entropy.</span>
-   <span class="signature">[`kurtosis( lambda )`][@stdlib/stats/base/dists/exponential/kurtosis]</span><span class="delimiter">: </span><span class="description">exponential distribution excess kurtosis.</span>
-   <span class="signature">[`mean( lambda )`][@stdlib/stats/base/dists/exponential/mean]</span><span class="delimiter">: </span><span class="description">exponential distribution expected value.</span>
-   <span class="signature">[`median( lambda )`][@stdlib/stats/base/dists/exponential/median]</span><span class="delimiter">: </span><span class="description">exponential distribution median.</span>
-   <span class="signature">[`mode( lambda )`][@stdlib/stats/base/dists/exponential/mode]</span><span class="delimiter">: </span><span class="description">exponential distribution mode.</span>
-   <span class="signature">[`skewness( lambda )`][@stdlib/stats/base/dists/exponential/skewness]</span><span class="delimiter">: </span><span class="description">exponential distribution skewness.</span>
-   <span class="signature">[`stdev( lambda )`][@stdlib/stats/base/dists/exponential/stdev]</span><span class="delimiter">: </span><span class="description">exponential distribution standard deviation.</span>
-   <span class="signature">[`variance( lambda )`][@stdlib/stats/base/dists/exponential/variance]</span><span class="delimiter">: </span><span class="description">exponential distribution variance.</span>

</div>

<!-- </toc> -->

The namespace contains a constructor function for creating an [exponential][exponential-distribution] distribution object.

<!-- <toc pattern="*ctor*"> -->

<div class="namespace-toc">

-   <span class="signature">[`Exponential( [lambda] )`][@stdlib/stats/base/dists/exponential/ctor]</span><span class="delimiter">: </span><span class="description">exponential distribution constructor.</span>

</div>

<!-- </toc> -->

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

var dist = new Exponential( 2.0 );

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

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- TODO: better examples -->

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

```javascript
var Float64Array = require( '@stdlib/array/float64' );
var randomExponential = require( '@stdlib/random/array/exponential' );
var dcusum = require( '@stdlib/blas/ext/base/dcusum' );
var exponential = require( '@stdlib/stats/base/dists/exponential' );

// Simulate interarrival times of customers entering a store:
var lambda = 0.5; // Average rate (customers per minute)
var numCustomers = 10;

// Generate interarrival times using the exponential distribution:
var interarrivalTimes = randomExponential( numCustomers, lambda, {
    'dtype': 'float64'
});

console.log( 'Simulated interarrival times for ' + numCustomers + ' customers: ' );
console.log( interarrivalTimes );

// Calculate cumulative arrival times by computing the cumulative sum of interarrival times:
var arrivalTimes = new Float64Array( interarrivalTimes.length );
dcusum( interarrivalTimes.length, 0.0, interarrivalTimes, 1, arrivalTimes, 1 );

console.log( '\nCustomer arrival times: ' );
console.log( arrivalTimes );

// Probability that a customer arrives within two minutes:
var x = 2.0;
var prob = exponential.cdf( x, lambda );
console.log( '\nProbability that a customer arrives within ' + x + ' minutes: ' + prob.toFixed(4) );

// Expected time until the next customer arrives:
var mean = exponential.mean( lambda );
console.log( 'Expected interarrival time: ' + mean + ' minutes' );

var dist = new exponential.Exponential( lambda );

var median = dist.median;
console.log( 'Median interarrival time: ' + median + ' minutes' );

// Evaluate the PDF at x = 1.0:
var out = dist.pdf( 1.0 );
console.log( 'PDF at x = 1: ' + out.toFixed(4) );

// Evaluate the MGF at t = 0.1:
out = dist.mgf( 0.1 );
console.log( 'MGF at t = 0.1: ' + out.toFixed(4) );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

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<section class="links">

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

<!-- <toc-links> -->

[@stdlib/stats/base/dists/exponential/ctor]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/ctor

[@stdlib/stats/base/dists/exponential/entropy]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/entropy

[@stdlib/stats/base/dists/exponential/kurtosis]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/kurtosis

[@stdlib/stats/base/dists/exponential/mean]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/mean

[@stdlib/stats/base/dists/exponential/median]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/median

[@stdlib/stats/base/dists/exponential/mode]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/mode

[@stdlib/stats/base/dists/exponential/skewness]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/skewness

[@stdlib/stats/base/dists/exponential/stdev]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/stdev

[@stdlib/stats/base/dists/exponential/variance]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/variance

[@stdlib/stats/base/dists/exponential/cdf]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/cdf

[@stdlib/stats/base/dists/exponential/logcdf]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/logcdf

[@stdlib/stats/base/dists/exponential/logpdf]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/logpdf

[@stdlib/stats/base/dists/exponential/mgf]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/mgf

[@stdlib/stats/base/dists/exponential/pdf]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/pdf

[@stdlib/stats/base/dists/exponential/quantile]: https://github.com/stdlib-js/stats/tree/main/base/dists/exponential/quantile

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</section>

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