@stdlib/stats-base-dists-levy-logpdf
v0.3.1TypeScript
Lévy distribution logarithm of probability density function (PDF).
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Published by The Stdlib Authors
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About stdlib...
Logarithm of Probability Density Function
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> [Lévy][levy-distribution] distribution logarithm of [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-logpdf
Usage
`javascript`
var logpdf = require( '@stdlib/stats-base-dists-levy-logpdf' );
#### logpdf( x, mu, c )
Evaluates the logarithm of the [probability density function][pdf] (PDF) for a [Lévy][levy-distribution] distribution with parameters mu (location parameter) and c (scale parameter).
`javascript
var y = logpdf( 2.0, 0.0, 1.0 );
// returns ~-2.209
y = logpdf( -1.0, 4.0, 4.0 );
// returns -Infinity
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = logpdf( NaN, 0.0, 1.0 );
// returns NaN
y = logpdf( 0.0, NaN, 1.0 );
// returns NaN
y = logpdf( 0.0, 0.0, NaN );
// returns NaN
`
If provided c <= 0, the function returns NaN.
`javascript
var y = logpdf( 2.0, 0.0, -1.0 );
// returns NaN
y = logpdf( 2.0, 0.0, 0.0 );
// returns NaN
`
#### logpdf.factory( mu, c )
Returns a function for evaluating the logarithm of the [probability density function][pdf] (PDF) of a [Lévy][levy-distribution] distribution with parameters mu (location parameter) and c (scale parameter).
`javascript
var mylogpdf = logpdf.factory( 10.0, 2.0 );
var y = mylogpdf( 11.0 );
// returns ~-1.572
y = mylogpdf( 20.0 );
// returns ~-4.126
`
Notes
- In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.
Examples
`javascript
var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var logpdf = require( '@stdlib/stats-base-dists-levy-logpdf' );
var mu;
var c;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
mu = randu() * 10.0;
x = ( randu()*10.0 ) + mu;
c = ( randu()*10.0 ) + EPS;
y = logpdf( x, mu, c );
console.log( 'x: %d, µ: %d, c: %d, ln(f(x;µ,c)): %d', x, mu, c, y );
}
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/levy/logpdf.h"
#### stdlib_base_dists_levy_logpdf( x, mu, c )
Evaluates the natural logarithm of the [probability density function][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_logpdf( 2.0, 0.0, 1.0 );
// returns ~-2.209
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_logpdf( const double x, const double mu, const double c );
$3
`c
#include "stdlib/stats/base/dists/levy/logpdf.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_logpdf( x, mu, c );
printf( "x: %lf, µ: %lf, c: %lf, ln(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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[levy-distribution]: https://en.wikipedia.org/wiki/L%C3%A9vy_distribution
[pdf]: https://en.wikipedia.org/wiki/Probability_density_function