@stdlib/stats-base-dists-laplace-logpdf
v0.3.1TypeScript
Laplace distribution logarithm of probability density function (PDF).
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About stdlib...
Logarithm of Probability Density Function
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> [Laplace][laplace-distribution] distribution logarithm of probability density function (PDF).
The [probability density function][pdf] (PDF) for a [Laplace][laplace-distribution] random variable is
where mu is the location parameter and b > 0 is the scale parameter (also called diversity).
Installation
``bash`
npm install @stdlib/stats-base-dists-laplace-logpdf
Usage
`javascript`
var logpdf = require( '@stdlib/stats-base-dists-laplace-logpdf' );
#### logpdf( x, mu, b )
Evaluates the logarithm of the [probability density function][pdf] (PDF) for a [Laplace][laplace-distribution] distribution with parameters mu (location parameter) and b > 0 (scale parameter).
`javascript
var y = logpdf( 2.0, 0.0, 1.0 );
// returns ~-2.693
y = logpdf( -1.0, 2.0, 3.0 );
// returns ~-2.792
y = logpdf( 2.5, 2.0, 3.0 );
// returns ~-1.958
`
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 b <= 0, the function returns NaN.
`javascript
var y = logpdf( 2.0, 0.0, -1.0 );
// returns NaN
y = logpdf( 2.0, 8.0, 0.0 );
// returns NaN
`
#### logpdf.factory( mu, b )
Returns a function for evaluating the logarithm of the [PDF][pdf] for a [Laplace][laplace-distribution] distribution with parameters mu (location parameter) and b > 0 (scale parameter).
`javascript
var mylogpdf = logpdf.factory( 10.0, 2.0 );
var y = mylogpdf( 10.0 );
// returns ~-1.386
y = mylogpdf( 5.0 );
// returns ~-3.886
y = mylogpdf( 12.0 );
// returns ~-2.386
`
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 uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var logpdf = require( '@stdlib/stats-base-dists-laplace-logpdf' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 100, 0.0, 10.0, opts );
var mu = uniform( 100, 0.0, 10.0, opts );
var b = uniform( 100, 0.0, 10.0, opts );
logEachMap( 'x: %0.4f, µ: %0.4f, b: %0.4f, ln(f(x;µ,b)): %0.4f', x, mu, b, logpdf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/laplace/logpdf.h"
#### stdlib_base_dists_laplace_logpdf( x, mu, b )
Evaluates the logarithm of the probability density function (PDF) for a Laplace distribution with location parameter mu and scale parameter b at a value x.
`c`
double out = stdlib_base_dists_laplace_logpdf( 2.0, 0.0, 1.0 );
// returns ~-2.693
The function accepts the following arguments:
- x: [in] double input value.[in] double
- mu: location parameter.[in] double
- b: rate parameter.
`c`
double stdlib_base_dists_laplace_logpdf( const double x, const double mu, const double b );
$3
`c
#include "stdlib/stats/base/dists/laplace/logpdf.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 b;
double x;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
mu = random_uniform( -5.0, 5.0 );
b = random_uniform( 0.0, 20.0 );
x = random_uniform( 0.0, 20.0 );
y = stdlib_base_dists_laplace_logpdf( x, mu, b );
printf( "x: %lf, µ: %lf, b: %lf, ln(f(x;µ,b)): %lf\n", x, mu, b, 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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[laplace-distribution]: https://en.wikipedia.org/wiki/Laplace_distribution
[pdf]: https://en.wikipedia.org/wiki/Probability_density_function