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About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Logarithm of Probability Density Function

NPM version Build Status Coverage Status

Evaluate the natural logarithm of the probability density function (PDF) for a Pareto (Type I) distribution.

The probability density function (PDF) for a Pareto (Type I) random variable is

$$f(x;\alpha,\beta) = \begin{cases} \frac{\alpha\,\beta^\alpha}{x^{\alpha+1}} & \text{ for }x\ge \beta \\ 0 & \text{otherwise} \end{cases}$$

where alpha > 0 is the shape parameter and beta > 0 is the scale parameter.

Usage

import logpdf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-pareto-type1-logpdf@esm/index.mjs';

You can also import the following named exports from the package:

import { factory } from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-pareto-type1-logpdf@esm/index.mjs';

logpdf( x, alpha, beta )

Evaluates the natural logarithm of the probability density function (PDF) for a Pareto (Type I) distribution with parameters alpha (shape parameter) and beta (scale parameter).

var y = logpdf( 4.0, 1.0, 1.0 );
// returns ~-2.773

y = logpdf( 20.0, 1.0, 10.0 );
// returns ~-3.689

y = logpdf( 7.0, 2.0, 6.0 );
// returns ~-1.561

y = logpdf( 7.0, 6.0, 3.0 );
// returns ~-5.238

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

y = logpdf( 1.5, 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 alpha <= 0, the function returns NaN.

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

y = logpdf( 2.0, 0.0, 0.5 );
// returns NaN

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

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

y = logpdf( 2.0, 0.5, 0.0 );
// returns NaN

logpdf.factory( alpha, beta )

Returns a function for evaluating the natural logarithm of the probability density function (PDF) (CDF) of a Pareto (Type I) distribution with parameters alpha (shape parameter) and beta (scale parameter).

var mylogpdf = logpdf.factory( 0.5, 0.5 );
var y = mylogpdf( 0.8 );
// returns ~-0.705

y = mylogpdf( 2.0 );
// returns ~-2.079

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

<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@esm/index.mjs';
import logpdf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-pareto-type1-logpdf@esm/index.mjs';

var alpha;
var beta;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 8.0;
    alpha = randu() * 4.0;
    beta = randu() * 4.0;
    y = logpdf( x, alpha, beta );
    console.log( 'x: %d, α: %d, β: %d, ln(f(x;α,β)): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}

</script>
</body>
</html>

Notice

This package is part of stdlib, a standard library 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.

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.