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feat: add stats/base/dists/anglit/quantile
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‎lib/node_modules/@stdlib/stats/base/dists/anglit/quantile/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2026 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Quantile Function
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> [Anglit][anglit-distribution] distribution [quantile function][quantile-function].
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<section class="intro">
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The [quantile function][quantile-function] for an [anglit][anglit-distribution] random variable is
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```math
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Q(p;\mu,\sigma) = \mu + \sigma\left( \sin^{-1}(\sqrt{p}) - \frac{\pi}{4} \right)
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```
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for `0 <= p <= 1`, where `μ` is the location parameter and `σ` is the scale parameter.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var quantile = require( '@stdlib/stats/base/dists/anglit/quantile' );
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```
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#### quantile( p, mu, sigma )
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Evaluates the [quantile function][quantile-function] for an [anglit][anglit-distribution] distribution with location parameter `mu` and scale parameter `sigma`.
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```javascript
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var y = quantile( 0.8, 0.0, 1.0 );
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// returns ~0.322
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y = quantile( 0.5, 4.0, 2.0 );
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// returns 4.0
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```
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If provided a probability `p` outside the interval `[0,1]`, the function returns `NaN`.
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```javascript
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var y = quantile( 1.9, 0.0, 1.0 );
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// returns NaN
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y = quantile( -0.1, 0.0, 1.0 );
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// returns NaN
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```
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If provided `NaN` as any argument, the function returns `NaN`.
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```javascript
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var y = quantile( NaN, 0.0, 1.0 );
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// returns NaN
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y = quantile( 0.2, NaN, 1.0 );
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// returns NaN
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y = quantile( 0.2, 0.0, NaN );
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// returns NaN
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```
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If provided `sigma < 0`, the function returns `NaN`.
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```javascript
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var y = quantile( 0.4, 0.0, -1.0 );
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// returns NaN
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```
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If `sigma` equals `0`, the function evaluates a degenerate distribution centered at `mu`.
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```javascript
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var y = quantile( 0.9, 3.0, 0.0 );
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// returns 3.0
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```
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#### quantile.factory( mu, sigma )
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Returns a function for evaluating the [quantile function][quantile-function] of an [anglit][anglit-distribution] distribution with location parameter `mu` and scale parameter `sigma`.
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```javascript
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var myquantile = quantile.factory( 4.0, 2.0 );
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var y = myquantile( 0.2 );
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// returns ~3.356
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y = myquantile( 0.9 );
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// returns ~4.927
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```
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var uniform = require( '@stdlib/random/array/uniform' );
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var logEachMap = require( '@stdlib/console/log-each-map' );
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var quantile = require( '@stdlib/stats/base/dists/anglit/quantile' );
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var opts = {
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'dtype': 'float64'
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};
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var p = uniform( 10, 0.0, 1.0, opts );
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var mu = uniform( 10, -5.0, 5.0, opts );
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var sigma = uniform( 10, 0.0, 5.0, opts );
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logEachMap( 'p: %lf, mu: %lf, sigma: %lf, Q(p;mu,sigma): %lf', p, mu, sigma, quantile );
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```
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</section>
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<!-- /.examples -->
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* * *
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<section class="c">
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## C APIs
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<section class="intro">
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</section>
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<!-- /.intro -->
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<section class="usage">
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### Usage
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```c
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#include "stdlib/stats/base/dists/anglit/quantile.h"
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```
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#### stdlib_base_dists_anglit_quantile( p, mu, sigma )
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Evaluates the [quantile function][quantile-function] for an [anglit][anglit-distribution] distribution with location parameter `mu` and scale parameter `sigma`.
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```c
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double out = stdlib_base_dists_anglit_quantile( 0.8, 0.0, 1.0 );
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// returns ~0.322
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```
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The function accepts the following arguments:
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- **p**: `[in] double` probability.
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- **mu**: `[in] double` location parameter.
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- **sigma**: `[in] double` scale parameter.
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```c
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double stdlib_base_dists_anglit_quantile( const double p, const double mu, const double sigma );
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<section class="examples">
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### Examples
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```c
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#include "stdlib/stats/base/dists/anglit/quantile.h"
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#include <stdlib.h>
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#include <stdio.h>
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static double random_uniform( const double min, const double max ) {
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double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
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return min + ( v * ( max - min ) );
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}
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int main( void ) {
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double result;
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double sigma;
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double mu;
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double p;
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int i;
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for ( i = 0; i < 10; i++ ) {
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p = random_uniform( 0.0, 1.0 );
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mu = random_uniform( -5.0, 5.0 );
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sigma = random_uniform( 0.0, 5.0 );
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result = stdlib_base_dists_anglit_quantile( p, mu, sigma );
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printf( "p: %lf, mu: %lf, sigma: %lf, Q(p;mu,sigma): %lf\n", p, mu, sigma, result );
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}
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}
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<section class="related">
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</section>
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<!-- /.related -->
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<section class="links">
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[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
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[anglit-distribution]: https://en.wikipedia.org/wiki/Anglit_distribution
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/dists/anglit/quantile/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2026 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var format = require( '@stdlib/string/format' );
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var pkg = require( './../package.json' ).name;
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var quantile = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var sigma;
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var opts;
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var idx;
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var mu;
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var p;
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var y;
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var i;
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opts = {
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'dtype': 'float64'
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};
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p = uniform( 100, 0.0, 1.0, opts );
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mu = uniform( 100, -20.0, 20.0, opts );
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sigma = uniform( 100, 0.0, 20.0, opts );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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idx = i % p.length;
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y = quantile( p[ idx ], mu[ idx ], sigma[ idx ] );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( format( '%s:factory', pkg ), function benchmark( b ) {
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var myQuantile;
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var sigma;
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var opts;
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var mu;
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var p;
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var y;
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var i;
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mu = 4.0;
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sigma = 3.0;
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myQuantile = quantile.factory( mu, sigma );
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opts = {
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'dtype': 'float64'
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};
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p = uniform( 100, 0.0, 1.0, opts );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = myQuantile( p[ i % p.length ] );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

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