@stdlib/stats/base/dists/logistic/quantile/README.md

Standard library statistical functions.

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# Quantile Function

> [Logistic][logistic-distribution] distribution [quantile function][quantile-function].

<section class="intro">

The [quantile function][quantile-function] for a [logistic][logistic-distribution] random variable is

<!-- <equation class="equation" label="eq:logistic_quantile_function" align="center" raw="Q(p;\mu,s)= \mu + s \ln \left( \frac{p}{1-p} \right )" alt="Quantile function for a logistic distribution."> -->

<div class="equation" align="center" data-raw-text="Q(p;\mu,s)= \mu + s \ln \left( \frac{p}{1-p} \right )" data-equation="eq:logistic_quantile_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/logistic/quantile/docs/img/equation_logistic_quantile_function.svg" alt="Quantile function for a logistic distribution.">
    <br>
</div>

<!-- </equation> -->

for `0 <= p < 1`, where `µ` is the location parameter and `s > 0` is the scale parameter.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### quantile( p, mu, s )

Evaluates the [quantile function][quantile-function] for a [logistic][logistic-distribution] distribution with parameters `mu` (location parameter) and `s` (scale parameter).

```javascript
var y = quantile( 0.5, 0.0, 1.0 );
// returns 0.0

y = quantile( 0.2, 4.0, 2.0 );
// returns ~1.227
```

If provided a probability `p` outside the interval `[0,1]`, the function returns `NaN`.

```javascript
var y = quantile( 1.9, 0.0, 1.0 );
// returns NaN

y = quantile( -0.1, 0.0, 1.0 );
// returns NaN
```

If provided `NaN` as any argument, the function returns `NaN`.

```javascript
var y = quantile( NaN, 0.0, 1.0 );
// returns NaN

y = quantile( 0.0, NaN, 1.0 );
// returns NaN

y = quantile( 0.0, 0.0, NaN );
// returns NaN
```

If provided `s < 0`, the function returns `NaN`.

```javascript
var y = quantile( 0.4, 0.0, -1.0 );
// returns NaN
```

If provided `s = 0`, the function evaluates the [quantile function][quantile-function] of a [degenerate distribution][degenerate-distribution] centered at `mu`.

```javascript
var y = quantile( 0.3, 8.0, 0.0 );
// returns 8.0

y = quantile( 0.9, 8.0, 0.0 );
// returns 8.0
```

#### quantile.factory( mu, s )

Returns a function for evaluating the [quantile function][quantile-function] of a [logistic][logistic-distribution] distribution with parameters `mu` and `s`.

```javascript
var myQuantile = quantile.factory( 10.0, 2.0 );

var y = myQuantile( 0.2 );
// returns ~7.227

y = myQuantile( 0.8 );
// returns ~12.773
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/stats/base/dists/logistic/quantile' );

var mu;
var s;
var p;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    mu = randu() * 10.0;
    s = randu() * 10.0;
    y = quantile( p, mu, s );
    console.log( 'p: %d, µ: %d, s: %d, Q(p;µ,s): %d', p, mu, s, y );
}
```

</section>

<!-- /.examples -->

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

<section class="related">

</section>

<!-- /.related -->

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<section class="links">

[logistic-distribution]: https://en.wikipedia.org/wiki/Logistic_distribution

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

[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution

</section>

<!-- /.links -->