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# expit

> Compute the [standard logistic][logistic-function] function.

<section class="intro">

The [standard logistic][logistic-function] function, also called the expit function, inverse logit, or sigmoid function, is defined as the [logistic][logistic-function] function with parameters (`k = 1`, `x0 = 0`, `L = 1`).

<!-- <equation class="equation" label="eq:expit_function" align="center" raw="\begin{aligned}\operatorname{expit}(x) &= \frac{1}{1+e^{-x}} \\ &= \frac{e^{x}}{e^{x}+1} \\ &= \frac{1}{2} + \frac{1}{2}\tanh\frac{x}{2} \end{aligned}" alt="Standard logistic function."> -->

<div class="equation" align="center" data-raw-text="\begin{aligned}\operatorname{expit}(x) &amp;= \frac{1}{1+e^{-x}} \\ &amp;= \frac{e^{x}}{e^{x}+1} \\ &amp;= \frac{1}{2} + \frac{1}{2}\tanh\frac{x}{2} \end{aligned}" data-equation="eq:expit_function">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/011d8b8e35ceb466ad31f5484e176ccaeaa087a2/lib/node_modules/@stdlib/math/base/special/expit/docs/img/equation_expit_function.svg" alt="Standard logistic function.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var expit = require( '@stdlib/math/base/special/expit' );
```

#### expit( x )

Computes the [standard logistic][logistic-function] function.

```javascript
var v = expit( 0.0 );
// returns ~0.5

v = expit( 1.0 );
// returns ~0.731

v = expit( -1.0 );
// returns ~0.269

v = expit( Infinity );
// returns 1.0

v = expit( NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var expit = require( '@stdlib/math/base/special/expit' );

var x;
var i;

for ( i = 0; i < 100; i++ ) {
    x = randu();
    console.log( 'expit(%d) = %d', x, expit( x ) );
}
```

</section>

<!-- /.examples -->

<section class="links">

[logistic-function]: https://en.wikipedia.org/wiki/Logistic_function

</section>

<!-- /.links -->
