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Logarithm of Probability Density Function

Weibull distribution logarithm of probability density function (PDF).

The probability density function (PDF) for a Weibull random variable is

$$f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} & x \geq 0 \\ 0 & x < 0\end{cases}$$

where lambda > 0 and k > 0 are the respective scale and shape parameters of the distribution.

Installation

npm install @stdlib/stats-base-dists-weibull-logpdf

Alternatively,

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

The branches.md 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

var logpdf = require( '@stdlib/stats-base-dists-weibull-logpdf' );

logpdf( x, k, lambda )

Evaluates the logarithm of the probability density function (PDF) for a Weibull distribution with shape parameter k and scale parameter lambda.

var y = logpdf( 2.0, 1.0, 0.5 );
// returns ~-3.307

y = logpdf( -1.0, 4.0, 2.0 );
// returns -Infinity

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

var y = logpdf( NaN, 1.0, 1.0 );
// returns NaN

y = logpdf( 0.0, NaN, 1.0 );
// returns NaN

y = logpdf( 0.0, 1.0, NaN );
// returns NaN

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

var y = logpdf( 2.0, 0.0, 1.0 );
// returns NaN

y = logpdf( 2.0, -1.0, 1.0 );
// returns NaN

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

var y = logpdf( 2.0, 1.0, 0.0 );
// returns NaN

y = logpdf( 2.0, 1.0, -1.0 );
// returns NaN

logpdf.factory( k, lambda )

Returns a function for evaluating the logarithm of the PDF for a Weibull distribution with shape parameter k and scale parameter lambda.

var mylogpdf = logpdf.factory( 2.0, 10.0 );

var y = mylogpdf( 12.0 );
// returns ~-2.867

y = mylogpdf( 5.0 );
// returns ~-2.553

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

var randu = require( '@stdlib/random-base-randu' );
var logpdf = require( '@stdlib/stats-base-dists-weibull-logpdf' );

var lambda;
var k;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    lambda = randu() * 10.0;
    k = randu() * 10.0;
    y = logpdf( x, k, lambda );
    console.log( 'x: %d, k: %d, λ: %d, ln(f(x;k,λ)): %d', x.toFixed( 4 ), k.toFixed( 4 ), lambda.toFixed( 4 ), y.toFixed( 4 ) );
}

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C APIs

Usage

#include "stdlib/stats/base/dists/weibull/logpdf.h"

stdlib_base_dists_weibull_logpdf( x, k, lambda )

Evaluates the logarithm of the probability density function (PDF) for a Weibull distribution with shape parameter k and scale parameter lambda.

double out = stdlib_base_dists_weibull_logpdf( 2.0, 1.0, 0.5 );
// returns ~3.307

The function accepts the following arguments:

• x: [in] double input value.
• k: [in] double shape parameter.
• lambda: [in] double scale parameter.

double stdlib_base_dists_weibull_logpdf( const double x, const double k, const double lambda );

Examples

#include "stdlib/stats/base/dists/weibull/logpdf.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 lambda;
    double x;
    double k;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0.0, 10.0 );
        lambda = random_uniform( 0.0, 10.0 );
        k = random_uniform( 0.0, 10.0 );
        y = stdlib_base_dists_weibull_logpdf( x, k, lambda );
        printf( "x: %lf, k: %lf, λ: %lf, ln(f(x;k,λ)): %lf\n", x, k, lambda, y );
    }
}

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Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.