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

Standard library statistical functions.

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# Quantile Function

> [F][f-distribution] distribution [quantile function][quantile-function].

<section class="intro">

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

<!-- <equation class="equation" label="eq:f_quantile_function" align="center" raw="Q(p;d_1,d_2) = \,\inf\left\{ x\in [0,+\infty) : p \le F(x;d_1,d_2) \right\}" alt="Quantile function for an F distribution."> -->

<div class="equation" align="center" data-raw-text="Q(p;d_1,d_2) = \,\inf\left\{ x\in [0,+\infty) : p \le F(x;d_1,d_2) \right\}" data-equation="eq:f_quantile_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/f/quantile/docs/img/equation_f_quantile_function.svg" alt="Quantile function for an F distribution.">
    <br>
</div>

<!-- </equation> -->

for `0 <= p < 1`, where `d1` is the numerator degrees of freedom, `d2` is the denominator degrees of freedom and `F` the cumulative distribution function (CDF) of the F distribution.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### quantile( p, d1, d2 )

Evaluates the [quantile function][quantile-function] for a [F][f-distribution] distribution with parameters `d1` (numerator degrees of freedom) and `d2` (denominator degrees of freedom).

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

y = quantile( 0.2, 4.0, 2.0 );
// returns ~0.405

y = quantile( 0.8, 4.0, 2.0 );
// returns ~4.236
```

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

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

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

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

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

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

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

If provided `d1 <= 0`, the function returns `NaN`.

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

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

If provided `d2 <= 0`, the function returns `NaN`.

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

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

#### quantile.factory( d1, d2 )

Returns a function for evaluating the quantile function of a [F][f-distribution] distribution with parameters `d1` (numerator degrees of freedom) and `d2` (denominator degrees of freedom).

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

var y = myquantile( 0.2 );
// returns ~0.527

y = myquantile( 0.8 );
// returns ~4.382
```

</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/f/quantile' );

var d1;
var d2;
var p;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    d1 = randu() * 10.0;
    d2 = randu() * 10.0;
    y = quantile( p, d1, d2 );
    console.log( 'p: %d, d1: %d, d2: %d, Q(p;d1,d2): %d', p.toFixed( 4 ), d1.toFixed( 4 ), d2.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">

[f-distribution]: https://en.wikipedia.org/wiki/F_distribution

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

</section>

<!-- /.links -->