@stdlib/stats-base-dists-levy-pdf
v0.3.1TypeScript
Lévy distribution probability density function (PDF).
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Published by The Stdlib Authors
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Probability Density Function
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> [Lévy][levy-distribution] distribution [probability density function (PDF)][pdf].
The [probability density function][pdf] (PDF) for a [Lévy][levy-distribution] random variable is
where μ is the location parameter and c > 0 is the scale parameter.
Installation
``bash`
npm install @stdlib/stats-base-dists-levy-pdf
Usage
`javascript`
var pdf = require( '@stdlib/stats-base-dists-levy-pdf' );
#### pdf( x, mu, c )
Evaluates the [probability density function][pdf] (PDF) for a [Lévy][levy-distribution] distribution with parameters mu (location parameter) and c (scale parameter).
`javascript
var y = pdf( 2.0, 0.0, 1.0 );
// returns ~0.11
y = pdf( -1.0, 4.0, 4.0 );
// returns 0.0
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = pdf( NaN, 0.0, 1.0 );
// returns NaN
y = pdf( 0.0, NaN, 1.0 );
// returns NaN
y = pdf( 0.0, 0.0, NaN );
// returns NaN
`
If provided c <= 0, the function returns NaN.
`javascript
var y = pdf( 2.0, 0.0, -1.0 );
// returns NaN
y = pdf( 2.0, 0.0, 0.0 );
// returns NaN
`
#### pdf.factory( mu, c )
Returns a function for evaluating the [probability density function][pdf] (PDF) of a [Lévy][levy-distribution] distribution with parameters mu (location parameter) and c (scale parameter).
`javascript
var mypdf = pdf.factory( 10.0, 2.0 );
var y = mypdf( 11.0 );
// returns ~0.208
y = mypdf( 20.0 );
// returns ~0.016
`
Examples
`javascript
var uniform = require( '@stdlib/random-base-uniform' );
var EPS = require( '@stdlib/constants-float64-eps' );
var pdf = require( '@stdlib/stats-base-dists-levy-pdf' );
var mu;
var c;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
mu = uniform( 0.0, 10.0 );
x = uniform( mu, mu + 10.0 );
c = uniform( EPS, 10.0 );
y = pdf( x, mu, c );
console.log( 'x: %d, µ: %d, c: %d, f(x;µ,c): %d', x, mu, c, y );
}
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/levy/pdf.h"
#### stdlib_base_dists_levy_pdf( x, mu, c )
Evaluates the [probability density][pdf] for a [Lévy][levy-distribution] distribution with input value x, location parameter mu, and scale parameter c.
`c`
double out = stdlib_base_dists_levy_pdf( 2.0, 0.0, 1.0 );
// returns ~0.11
The function accepts the following arguments:
- x: [in] double input value.[in] double
- mu: location parameter.[in] double
- c: scale parameter.
`c`
double stdlib_base_dists_levy_pdf( const double x, const double mu, const double c );
$3
`c
#include "stdlib/stats/base/dists/levy/pdf.h"
#include "stdlib/constants/float64/eps.h"
#include
#include
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 mu;
double x;
double c;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
mu = random_uniform( 0.0, 10.0 );
x = random_uniform( mu, mu + 10.0 );
c = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
y = stdlib_base_dists_levy_pdf( x, mu, c );
printf( "x: %lf, µ: %lf, c: %lf, f(x;µ,c): %lf\n", x, mu, c, 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 © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-levy-pdf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-levy-pdf/blob/deno/README.md
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-levy-pdf/main/LICENSE
[levy-distribution]: https://en.wikipedia.org/wiki/L%C3%A9vy_distribution
[pdf]: https://en.wikipedia.org/wiki/Probability_density_function