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feat: add implementation of stats/base/dists/halfnormal/kurtosis
PR-URL: #9771 Ref: #9416 Co-authored-by: Philipp Burckhardt <[email protected]> Reviewed-by: Philipp Burckhardt <[email protected]>
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‎lib/node_modules/@stdlib/stats/base/dists/halfnormal/kurtosis/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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# Kurtosis
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> [Half-normal][halfnormal-distribution] distribution [excess kurtosis][kurtosis].
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<section class="intro">
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The [excess kurtosis][kurtosis] of a [half-normal][halfnormal-distribution] distribution with scale `sigma > 0` is
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<!-- <equation class="equation" label="eq:halfnormal_kurtosis" align="center" raw="\gamma_2 = \frac{8(\pi-3)}{(\pi-2)^2}" alt="Excess kurtosis for a half-normal distribution."> -->
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```math
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\gamma_2 = \frac{8(\pi-3)}{(\pi-2)^2}
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```
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<!-- <div class="equation" align="center" data-raw-text="\gamma_2 = \frac{8(\pi-3)}{(\pi-2)^2}" data-equation="eq:halfnormal_kurtosis">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@2d398018e6a1275033c4ad59453a233302c3409d/lib/node_modules/@stdlib/stats/base/dists/halfnormal/kurtosis/docs/img/equation_halfnormal_kurtosis.svg" alt="Excess kurtosis for a half-normal distribution.">
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<br>
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</div> -->
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<!-- </equation> -->
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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 kurtosis = require( '@stdlib/stats/base/dists/halfnormal/kurtosis' );
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```
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#### kurtosis( sigma )
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Returns the [excess kurtosis][kurtosis] of a [half-normal][halfnormal-distribution] distribution with scale parameter `sigma`.
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```javascript
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var x = kurtosis( 1.0 );
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// returns ~0.869
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var y = kurtosis( 4.0 );
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// returns ~0.869
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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 x = kurtosis( 0.0 );
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// returns NaN
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var y = kurtosis( -1.0 );
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// returns NaN
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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 kurtosis = require( '@stdlib/stats/base/dists/halfnormal/kurtosis' );
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var opts = {
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'dtype': 'float64'
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};
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var sigma = uniform( 10, 0.0, 20.0, opts );
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logEachMap( 'σ: %0.4f, Kurt(X;σ): %0.4f', sigma, kurtosis );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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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/halfnormal/kurtosis.h"
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```
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#### stdlib_base_dists_halfnormal_kurtosis( sigma )
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Returns the [excess kurtosis][kurtosis] of a [half-normal][halfnormal-distribution] distribution with scale parameter `sigma`.
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```c
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double out = stdlib_base_dists_halfnormal_kurtosis( 1.0 );
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// returns ~0.869
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```
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The function accepts the following arguments:
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- **sigma**: `[in] double` scale parameter.
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```c
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double stdlib_base_dists_halfnormal_kurtosis( const double sigma );
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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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/halfnormal/kurtosis.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 sigma;
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double y;
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int i;
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for ( i = 0; i < 10; i++ ) {
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sigma = random_uniform( 0.0, 20.0 );
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y = stdlib_base_dists_halfnormal_kurtosis( sigma );
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printf( "σ: %lf, Kurt(σ): %lf\n", sigma, y );
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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 for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[halfnormal-distribution]: https://en.wikipedia.org/wiki/Half-normal_distribution
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[kurtosis]: https://en.wikipedia.org/wiki/Kurtosis
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/dists/halfnormal/kurtosis/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 Float64Array = require( '@stdlib/array/float64' );
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var uniform = require( '@stdlib/random/base/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var EPS = require( '@stdlib/constants/float64/eps' );
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var pkg = require( './../package.json' ).name;
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var kurtosis = 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 len;
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var y;
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var i;
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len = 100;
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sigma = new Float64Array( len );
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for ( i = 0; i < len; i++ ) {
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sigma[ i ] = uniform( EPS, 10.0 );
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}
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = kurtosis( sigma[ i % len ] );
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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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});

‎lib/node_modules/@stdlib/stats/base/dists/halfnormal/kurtosis/benchmark/benchmark.native.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 resolve = require( 'path' ).resolve;
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var bench = require( '@stdlib/bench' );
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var Float64Array = require( '@stdlib/array/float64' );
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var uniform = require( '@stdlib/random/base/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var EPS = require( '@stdlib/constants/float64/eps' );
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var tryRequire = require( '@stdlib/utils/try-require' );
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var pkg = require( './../package.json' ).name;
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// VARIABLES //
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var kurtosis = tryRequire( resolve( __dirname, './../lib/native.js' ) );
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var opts = {
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'skip': ( kurtosis instanceof Error )
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};
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// MAIN //
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bench( pkg+'::native', opts, function benchmark( b ) {
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var sigma;
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var len;
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var y;
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var i;
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len = 100;
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sigma = new Float64Array( len );
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for ( i = 0; i < len; i++ ) {
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sigma[ i ] = uniform( EPS, 10.0 );
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}
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = kurtosis( sigma[ i % len ] );
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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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