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

Standard library statistical functions.

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# Quantile Function

> [Geometric][geometric-distribution] distribution [quantile function][quantile-function].

<section class="intro">

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

<!-- <equation class="equation" label="eq:geometric_quantile_function" align="center" raw="Q(r;p)=\left\lceil \frac{\ln(1-r)}{\ln(1-p)} \right\rceil" alt="Quantile function for a geometric distribution."> -->

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

<!-- </equation> -->

for `0 < r < 1`, where `p` is the success probability.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### quantile( r, p )

Evaluates the [quantile function][quantile-function] for a [geometric][geometric-distribution] distribution with success probability `p` at a value `r`.

```javascript
var y = quantile( 0.8, 0.4 );
// returns 3

y = quantile( 0.5, 0.4 );
// returns 1

y = quantile( 0.9, 0.1 );
// returns 21
```

If provided an input probability `r` outside the interval `[0,1]`, the function returns `NaN`.

```javascript
var y = quantile( 1.9, 0.5 );
// returns NaN

y = quantile( -0.1, 0.5 );
// returns NaN
```

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

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

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

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

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

y = quantile( 0.4, 1.5 );
// returns NaN
```

#### quantile.factory( p )

Returns a function for evaluating the [quantile function][quantile-function] for a [geometric][geometric-distribution] distribution with success probability `p`.

```javascript
var myquantile = quantile.factory( 0.4 );
var y = myquantile( 0.4 );
// returns 0

y = myquantile( 0.8 );
// returns 3

y = myquantile( 1.0 );
// returns Infinity
```

</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/geometric/quantile' );

var p;
var r;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    r = randu();
    p = randu();
    y = quantile( r, p );
    console.log( 'r: %d, p: %d, Q(r;p): %d', r.toFixed( 4 ), p.toFixed( 4 ), y.toFixed( 4 ) );
}
```

</section>

<!-- /.examples -->

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

<section class="related">

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[geometric-distribution]: https://en.wikipedia.org/wiki/Geometric_distribution

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

</section>

<!-- /.links -->