@stdlib/stats/base/dists/discrete-uniform/quantile/README.md

Standard library statistical functions.

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# Quantile Function

> [Discrete uniform][discrete-uniform-distribution] distribution [quantile function][quantile-function].

<section class="intro">

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

<!-- <equation class="equation" label="eq:discrete_uniform_quantile_function" align="center" raw="Q(p) = a + \lfloor p \cdot ( b - a + 1 ) \rfloor" alt="Quantile function for a discrete uniform distribution."> -->

<div class="equation" align="center" data-raw-text="Q(p) = a + \lfloor p \cdot ( b - a + 1 ) \rfloor" data-equation="eq:discrete_uniform_quantile_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/discrete-uniform/quantile/docs/img/equation_discrete_uniform_quantile_function.svg" alt="Quantile function for a discrete uniform distribution.">
    <br>
</div>

<!-- </equation> -->

for `0 <= p <= 1`, where `a` is the minimum support and `b` is the maximum support. The parameters must satisfy `a <= b`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### quantile( p, a, b )

Evaluates the [quantile function][quantile-function] for a [discrete uniform][discrete-uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).

```javascript
var y = quantile( 0.8, 0, 1 );
// returns 1

y = quantile( 0.5, 0, 10 );
// returns 5
```

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

```javascript
var y = quantile( 1.9, 0, 2 );
// returns NaN

y = quantile( -0.1, 0, 2 );
// returns NaN
```

If `a` or `b` is not an integer value, the function returns `NaN`.

```javascript
var y = quantile( 0.2, 1, 5.5 );
// returns NaN
```

If provided `a > b`, the function returns `NaN`.

```javascript
var y = quantile( 0.4, 2, 1 );
// 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
```

#### quantile.factory( a, b )

Returns a function for evaluating the quantile function of a [discrete uniform][discrete-uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).

```javascript
var myquantile = quantile.factory( 0, 4 );
var y = myquantile( 0.8 );
// returns 4

y = myquantile( 0.3 );
// returns 1
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var randint = require( '@stdlib/random/base/discrete-uniform' );
var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/stats/base/dists/discrete-uniform/quantile' );

var randa = randint.factory( 0, 5 );
var randb = randint.factory();
var a;
var b;
var p;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    a = randa();
    b = randb( a, a+randa() );
    v = quantile( p, a, b );
    console.log( 'p: %d, a: %d, b: %d, Q(p;a,b): %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), v.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">

[discrete-uniform-distribution]: https://en.wikipedia.org/wiki/Discrete_uniform_distribution

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

</section>

<!-- /.links -->