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

Standard library statistical functions.

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# Quantile Function

> [Triangular][triangular-distribution] distribution [quantile function][quantile-function].

<section class="intro">

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

<!-- <equation class="equation" label="eq:triangular_quantile_function" align="center" raw="Q(p;a,b,c) = \begin{cases} a + \sqrt{(b-a)(c-a)p} & \text{ for } 0 \le p \le F(c) \\ b - \sqrt{(b-a)(b-c)(1-p)} & \text{ for } F(c) \le p \le 1 \end{cases}" alt="Quantile function for a triangular distribution."> -->

<div class="equation" align="center" data-raw-text="Q(p;a,b,c) = \begin{cases} a + \sqrt{(b-a)(c-a)p} &amp; \text{ for } 0 \le p \le F(c) \\ b - \sqrt{(b-a)(b-c)(1-p)} &amp; \text{ for } F(c) \le p \le 1 \end{cases}" data-equation="eq:triangular_quantile_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/triangular/quantile/docs/img/equation_triangular_quantile_function.svg" alt="Quantile function for a triangular distribution.">
    <br>
</div>

<!-- </equation> -->

where `a` is the lower limit, `b` is the upper limit and `c` is the mode.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

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

Evaluates the [quantile function][quantile-function] for a [triangular][triangular-distribution] distribution with parameters `a` (lower limit), `b` (upper limit) and `c` (mode).

```javascript
var y = quantile( 0.9, -1.0, 1.0, 0.0 );
// returns ~0.553

y = quantile( 0.1, -1.0, 1.0, 0.5 );
// returns ~-0.452

y = quantile( 0.1, -20.0, 0.0, -2.0 );
// returns -14.0

y = quantile( 0.8, 0.0, 20.0, 0.0 );
// returns ~11.056
```

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

```javascript
var y = quantile( 1.9, 0.0, 1.0, 0.5 );
// returns NaN

y = quantile( -0.1, 0.0, 1.0, 0.5 );
// returns NaN
```

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

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

y = quantile( 0.1, NaN, 1.0, 0.5 );
// returns NaN

y = quantile( 0.1, 0.0, NaN, 0.5 );
// returns NaN

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

If provided parameters not satisfying `a <= c <= b`, the function returns `NaN`.

```javascript
var y = quantile( 0.1, 1.0, 0.0, 1.5 );
// returns NaN

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

y = quantile( 0.1, 0.0, -1.0, 0.5 );
// returns NaN
```

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

Returns a function for evaluating the [quantile function][quantile-function] of a [triangular][triangular-distribution] distribution with parameters `a` (lower limit), `b` (upper limit) and `c` (mode).

```javascript
var myquantile = quantile.factory( 2.0, 4.0, 2.5 );
var y = myquantile( 0.4 );
// returns ~2.658

y = myquantile( 0.8 );
// returns ~3.225
```

</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/triangular/quantile' );

var a;
var b;
var c;
var p;
var y;
var i;

for ( i = 0; i < 25; i++ ) {
    p = randu();
    a = randu() * 10.0;
    b = a + (randu() * 40.0);
    c = a + ((b-a) * randu());
    y = quantile( p, a, b, c );
    console.log( 'p: %d, a: %d, b: %d, c: %d, Q(p;a,b,c): %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), c.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">

[triangular-distribution]: https://en.wikipedia.org/wiki/Triangular_distribution

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

</section>

<!-- /.links -->