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

Standard library statistical functions.

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# Quantile Function

> [Weibull][weibull-distribution] distribution [quantile function][quantile-function].

<section class="intro">

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

<!-- <equation class="equation" label="eq:weibull_quantile_function" align="center" raw="Q(p;k,\lambda) = \lambda {(-\ln(1-p))}^{1/k}" alt="Quantile function for a Weibull distribution."> -->

<div class="equation" align="center" data-raw-text="Q(p;k,\lambda) = \lambda {(-\ln(1-p))}^{1/k}" data-equation="eq:weibull_quantile_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/weibull/quantile/docs/img/equation_weibull_quantile_function.svg" alt="Quantile function for a Weibull distribution.">
    <br>
</div>

<!-- </equation> -->

for `0 <= p < 1`, where `lambda > 0` is the [shape parameter][shape] and `k > 0` is the [scale parameter][scale].

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### quantile( p, k, lambda )

Evaluates the [quantile function][quantile-function] for a [Weibull][weibull-distribution] distribution with [shape parameter][shape] `k` and [scale parameter][scale] `lambda`.

```javascript
var y = quantile( 0.5, 1.0, 1.0 );
// returns ~0.693

y = quantile( 0.2, 2.0, 4.0 );
// returns ~1.89
```

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 `k <= 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 `lambda <= 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( k, lambda )

Returns a function for evaluating the quantile function of a [Weibull][weibull-distribution] distribution with [shape parameter][shape] `k` and [scale parameter][scale] `lambda`.

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

var y = myquantile( 0.2 );
// returns ~4.724

y = myquantile( 0.8 );
// returns ~12.686
```

</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/weibull/quantile' );

var lambda;
var k;
var p;
var y;
var i;

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

</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">

[weibull-distribution]: https://en.wikipedia.org/wiki/Weibull_distribution

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

[shape]: https://en.wikipedia.org/wiki/Shape_parameter

[scale]: https://en.wikipedia.org/wiki/Scale_parameter

</section>

<!-- /.links -->