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feat: add stats/base/dists/log-logistic/mode
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‎lib/node_modules/@stdlib/stats/base/dists/log-logistic/mode/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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# Mode
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> [Log-logistic][log-logistic-distribution] distribution [mode][mode].
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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 [mode][mode] for a [log-logistic][log-logistic-distribution] random variable with scale `α > 0` and shape `β > 1` is
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<!-- <equation class="equation" label="eq:log-logistic_mode" align="center" raw="\mathop{\mathrm{mode}}\left( X \right) = \alpha \left( \frac{\beta - 1}{\beta + 1} \right)^{1/\beta}" alt="Mode for a log-logistic distribution."> -->
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```math
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\mathop{\mathrm{mode}}\left( X \right) = \alpha \left( \frac{\beta - 1}{\beta + 1} \right)^{1/\beta}
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```
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<!-- <div class="equation" align="center" data-raw-text="\mathop{\mathrm{mode}}\left( X \right) = \alpha \left( \frac{\beta - 1}{\beta + 1} \right)^{1/\beta}" data-equation="eq:log-logistic_mode">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/log-logistic/mode/docs/img/equation_log_logistic_mode.svg" alt="Mode for a log-logistic 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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<!-- 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 mode = require( '@stdlib/stats/base/dists/log-logistic/mode' );
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```
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#### mode( alpha, beta )
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Returns the [mode][mode] for a [log-logistic][log-logistic-distribution] distribution with scale parameter `alpha` and shape parameter `beta`.
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```javascript
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var y = mode( 1.0, 2.0 );
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// returns ~0.577
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y = mode( 4.0, 3.0 );
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// returns ~3.175
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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 = mode( NaN, 2.0 );
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// returns NaN
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y = mode( 2.0, NaN );
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// returns NaN
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```
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If provided `alpha <= 0`, the function returns `NaN`.
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```javascript
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var y = mode( 0.0, 2.0 );
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// returns NaN
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y = mode( -1.0, 2.0 );
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// returns NaN
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```
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If provided `beta <= 0`, the function returns `NaN`.
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```javascript
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var y = mode( 2.0, 0.0 );
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// returns NaN
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y = mode( 2.0, -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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<!-- 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 mode = require( '@stdlib/stats/base/dists/log-logistic/mode' );
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var opts = {
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'dtype': 'float64'
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};
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var alpha = uniform( 10, 0.1, 10.0, opts );
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var beta = uniform( 10, 1.1, 10.0, opts );
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logEachMap( 'alpha: %0.4f, beta: %0.4f, Mode(X;alpha,beta): %0.4f', alpha, beta, mode );
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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/log-logistic/mode.h"
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```
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#### stdlib_base_dists_log_logistic_mode( alpha, beta )
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Returns the mode for a log-logistic distribution with scale `alpha` and shape `beta`.
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```c
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double out = stdlib_base_dists_log_logistic_mode( 1.0, 2.0 );
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// returns ~0.577
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```
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The function accepts the following arguments:
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- **alpha**: `[in] double` scale parameter.
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- **beta**: `[in] double` shape parameter.
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```c
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double stdlib_base_dists_log_logistic_mode( const double alpha, const double beta );
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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/log-logistic/mode.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 alpha;
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double beta;
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double v;
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int i;
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for ( i = 0; i < 25; i++ ) {
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alpha = random_uniform( 0.1, 10.0 );
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beta = random_uniform( 1.1, 10.0 );
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v = stdlib_base_dists_log_logistic_mode( alpha, beta );
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printf( "alpha: %lf, beta: %lf, Mode(X;alpha,beta): %lf\n", alpha, beta, v );
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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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[log-logistic-distribution]: https://en.wikipedia.org/wiki/Log-logistic_distribution
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[mode]: https://en.wikipedia.org/wiki/Mode
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/dists/log-logistic/mode/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( '@stdlib/stats/base/dists/log-logistic/mode/package.json' ).name;
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var mode = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var alpha;
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var beta;
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var opts;
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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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alpha = uniform( 100, EPS, 10.0, opts );
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beta = uniform( 100, 1.1, 10.0, opts );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = mode( alpha[ i % alpha.length ], beta[ i % beta.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/log-logistic/mode/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 tryRequire = require( '@stdlib/utils/try-require' );
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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 format = require( '@stdlib/string/format' );
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var pkg = require( '@stdlib/stats/base/dists/log-logistic/mode/package.json' ).name;
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// VARIABLES //
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var mode = tryRequire( resolve( __dirname, './../lib/native.js' ) );
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var opts = {
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'skip': ( mode 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 alpha;
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var beta;
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var opts;
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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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alpha = uniform( 100, EPS, 10.0, opts );
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beta = uniform( 100, 1.1, 10.0, opts );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = mode( alpha[ i % alpha.length ], beta[ i % beta.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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