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feat: add implementation of stats/base/dists/wald/kurtosis
PR-URL: #10216 Ref: #209 Co-authored-by: Philipp Burckhardt <pburckhardt@outlook.com> Reviewed-by: Philipp Burckhardt <pburckhardt@outlook.com> Signed-off-by: Bhargav Dabhade <bhargava2005dabhade@gmail.com> Signed-off-by: Philipp Burckhardt <pburckhardt@outlook.com>
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‎lib/node_modules/@stdlib/stats/base/dists/wald/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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> [Wald][wald-distribution] distribution [excess kurtosis][kurtosis].
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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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The [excess kurtosis][kurtosis] for a [Wald][wald-distribution] random variable with mean `μ` and shape parameter `λ > 0` is
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<!-- <equation class="equation" label="eq:wald_kurtosis" align="center" raw="\mathop{\mathrm{Kurt}}\left( X \right) = \frac{15\mu}{\lambda}" alt="Excess kurtosis for a Wald distribution."> -->
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```math
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\mathop{\mathrm{Kurt}}\left( X \right) = \frac{15\mu}{\lambda}
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```
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<!-- <div class="equation" align="center" data-raw-text="\mathop{\mathrm{Kurt}}\left( X \right) = \frac{15\mu}{\lambda}" data-equation="eq:wald_kurtosis">
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</div> -->
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<!-- Package usage documentation. -->
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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/wald/kurtosis' );
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```
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#### kurtosis( mu, lambda )
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Returns the [excess kurtosis][kurtosis] for a [Wald][wald-distribution] distribution with parameters `mu` (mean) and `lambda` (shape parameter).
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```javascript
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var y = kurtosis( 2.0, 1.0 );
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// returns 30.0
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y = kurtosis( 0.0, 1.0 );
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// returns NaN
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y = kurtosis( -1.0, 4.0 );
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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 = kurtosis( NaN, 1.0 );
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// returns NaN
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y = kurtosis( 0.0, NaN );
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// returns NaN
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```
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If provided `mu <= 0` or `lambda <= 0`, the function returns `NaN`.
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```javascript
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var y = kurtosis( 0.0, 0.0 );
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// returns NaN
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y = kurtosis( 0.0, -1.0 );
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// returns NaN
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y = kurtosis( -1.0, 0.0 );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<!-- Package 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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<!-- Package usage examples. -->
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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 EPS = require( '@stdlib/constants/float64/eps' );
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var kurtosis = require( '@stdlib/stats/base/dists/wald/kurtosis' );
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var opts = {
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'dtype': 'float64'
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};
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var mu = uniform( 10, EPS, 10.0, opts );
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var lambda = uniform( 10, EPS, 20.0, opts );
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logEachMap( 'µ: %0.4f, λ: %0.4f, Kurtosis(X;µ,λ): %0.4f', mu, lambda, 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/wald/kurtosis.h"
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```
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#### stdlib_base_dists_wald_kurtosis( mu, lambda )
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Returns the [excess kurtosis][kurtosis] for a [Wald][wald-distribution] distribution with mean `mu` and shape parameter `lambda`.
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```c
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double out = stdlib_base_dists_wald_kurtosis( 2.0, 1.0 );
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// returns 30.0
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```
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The function accepts the following arguments:
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- **mu**: `[in] double` mean.
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- **lambda**: `[in] double` shape parameter.
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```c
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double stdlib_base_dists_wald_kurtosis( const double mu, const double lambda );
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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/wald/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 lambda;
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double mu;
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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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mu = random_uniform( 0.1, 5.0 );
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lambda = random_uniform( 0.1, 20.0 );
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y = stdlib_base_dists_wald_kurtosis( mu, lambda );
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printf( "µ: %.4f, λ: %.4f, Kurtosis(X;µ,λ): %.4f\n", mu, lambda, 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 to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="references">
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</section>
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<!-- /.references -->
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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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[wald-distribution]: https://en.wikipedia.org/wiki/Inverse_Gaussian_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/wald/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 uniform = require( '@stdlib/random/array/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 lambda;
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var opts;
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var mu;
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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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mu = uniform( 100, EPS, 100.0, opts );
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lambda = uniform( 100, EPS, 20.0, opts );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = kurtosis( mu[ i % mu.length ], lambda[ i % lambda.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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});

‎lib/node_modules/@stdlib/stats/base/dists/wald/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 uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var tryRequire = require( '@stdlib/utils/try-require' );
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var format = require( '@stdlib/string/format' );
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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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// 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( format( '%s::native', pkg ), opts, function benchmark( b ) {
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var arrayOpts;
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var lambda;
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var mu;
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var y;
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var i;
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arrayOpts = {
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'dtype': 'float64'
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};
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mu = uniform( 100, EPS, 100.0, arrayOpts );
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lambda = uniform( 100, EPS, 20.0, arrayOpts );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = kurtosis( mu[ i % mu.length ], lambda[ i % lambda.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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