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Mode

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

[Cauchy][cauchy-distribution] distribution [mode][mode].

The [mode][mode] for a [Cauchy][cauchy-distribution] random variable with location parameter x0 and scale parameter Ɣ > 0 is

math
\mathop{\mathrm{mode}}\left( X \right) = x_0

## Installation

bash
npm install @stdlib/stats-base-dists-cauchy-mode

Alternatively,

- To load the package in a website via a script tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [deno][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [umd][umd-url] branch (see [README][umd-readme]).

The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

## Usage

javascript
var mode = require( '@stdlib/stats-base-dists-cauchy-mode' );

#### mode( x0, gamma )

Returns the [mode][mode] of a [Cauchy][cauchy-distribution] distribution with location parameter x0 and scale parameter gamma.

javascript
var v = mode( 10.0, 5.0 );
// returns 10.0

v = mode( 7.0, 2.0 );
// returns 7.0

If provided NaN as any argument, the function returns NaN.

javascript
var v = mode( NaN, 5.0 );
// returns NaN

v = mode( 20.0, NaN );
// returns NaN

If provided gamma <= 0, the function returns NaN.

javascript
var v = mode( 1.0, -1.0 );
// returns NaN

v = mode( 1.0, 0.0 );
// returns NaN

## Examples

javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var mode = require( '@stdlib/stats-base-dists-cauchy-mode' );

var opts = {
    'dtype': 'float64'
};
var gamma = uniform( 10, EPS, 10.0, opts );
var x0 = uniform( 10, 0.0, 100.0, opts );

logEachMap( 'x0: %0.4f, γ: %0.4f, mode(X;x0,γ): %0.4f', x0, gamma, mode );

## C APIs

### Usage

c
#include "stdlib/stats/base/dists/cauchy/mode.h"

#### stdlib_base_dists_cauchy_mode( x0, gamma )

Evaluates the [mode][mode] of a [Cauchy][cauchy-distribution] distribution with location parameter x0 and scale parameter gamma.

c
double out = stdlib_base_dists_cauchy_mode( 10.0, 5.0 );
// returns 10.0

The function accepts the following arguments:

- x0: [in] double location parameter.
- gamma: [in] double scale parameter.

c
double stdlib_base_dists_cauchy_mode( const double x0, const double gamma );

### Examples

c
#include "stdlib/stats/base/dists/cauchy/mode.h"
#include "stdlib/constants/float64/eps.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double gamma;
    double x0;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x0 = random_uniform( 0.0, 100.0 );
        gamma = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        y = stdlib_base_dists_cauchy_mode( x0, gamma );
        printf( "x0: %lf, γ: %lf, mode(X;x0,γ): %lf\n", x0, gamma, y );
    }
}

*

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

—-

## License

See [LICENSE][stdlib-license].

## Copyright

Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].