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][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> Evaluate the natural logarithm of the probability density function (PDF) for an [inverse gamma][inverse-gamma] distribution.

The [probability density function][pdf] (PDF) for an [inverse gamma][inverse-gamma] random variable is

Probability density function (PDF) for an inverse gamma distribution.

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

Installation

``bash npm install @stdlib/stats-base-dists-invgamma-logpdf`

`Usage`

`javascript var logpdf = require( '@stdlib/stats-base-dists-invgamma-logpdf' );`

#### logpdf( x, alpha, beta )

Evaluates the natural logarithm of the [probability density function][pdf] (PDF) for an [inverse gamma][inverse-gamma] distribution with parameters alpha (shape parameter) and beta (rate parameter).

`javascript var y = logpdf( 2.0, 0.5, 1.0 ); // returns ~-2.112

y = logpdf( 0.2, 1.0, 1.0 ); // returns ~-1.781

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

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

`javascript 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.

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

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

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

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

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

#### logpdf.factory( alpha, beta )

Returns a function for evaluating the natural logarithm of the [PDF][pdf] for an [inverse gamma][inverse-gamma] distribution with parameters alpha (shape parameter) and beta (rate parameter).

`javascript var mylogPDF = logpdf.factory( 6.0, 7.0 );

var y = mylogPDF( 2.0 ); // returns ~-1.464`

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var logpdf = require( '@stdlib/stats-base-dists-invgamma-logpdf' );

var opts = { 'dtype': 'float64' }; var x = uniform( 10, 0.0, 2.0, opts ); var alpha = uniform( 10, 0.0, 5.0, opts ); var beta = uniform( 10, 0.0, 5.0, opts );

logEachMap( 'x: %0.4f, α: %0.4f, β: %0.4f, ln(f(x;α,β)): %0.4f', x, alpha, beta, logpdf );`

*

`C APIs`

`$3`

`c #include "stdlib/stats/base/dists/invgamma/logpdf.h"`

#### stdlib_base_dists_invgamma_logpdf( alpha, beta )

Evaluates the natural logarithm of the probability density function (PDF) for an inverse gamma distribution with shape parameter alpha and scale parameter beta at a value x.

`c double out = stdlib_base_dists_invgamma_logpdf( 2.0, 0.5, 1.0 ); // returns ~-2.112`

The function accepts the following arguments:

- x: [in] doubleinput value. - alpha:[in] doubleshape parameter. - beta:[in] double scale parameter.

`c double stdlib_base_dists_invgamma_logpdf( const double x, const double mu, const double b );`

`$3`

`c #include "stdlib/stats/base/dists/laplace/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 alpha; double beta; double x; double y; int i;

for ( i = 0; i < 25; i++ ) { x = random_uniform( 0.0, 10.0 ); alpha = random_uniform( 0.0, 10.0 ); beta = random_uniform( 0.0, 10.0 ); y = stdlib_base_dists_invgamma_logpdf( x, alpha, beta ); printf( "x: %lf, α: %lf, β: %lf, ln(f(x;α,β)): %lf\n", x, alpha, beta, 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`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-invgamma-logpdf.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-invgamma-logpdf

[test-image]: https://github.com/stdlib-js/stats-base-dists-invgamma-logpdf/actions/workflows/test.yml/badge.svg?branch=v0.3.1 [test-url]: https://github.com/stdlib-js/stats-base-dists-invgamma-logpdf/actions/workflows/test.yml?query=branch:v0.3.1

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-invgamma-logpdf/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-invgamma-logpdf?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/stats-base-dists-invgamma-logpdf/tree/deno [deno-readme]: https://github.com/stdlib-js/stats-base-dists-invgamma-logpdf/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/stats-base-dists-invgamma-logpdf/tree/umd [umd-readme]: https://github.com/stdlib-js/stats-base-dists-invgamma-logpdf/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/stats-base-dists-invgamma-logpdf/tree/esm [esm-readme]: https://github.com/stdlib-js/stats-base-dists-invgamma-logpdf/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/stats-base-dists-invgamma-logpdf/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-invgamma-logpdf/main/LICENSE

[inverse-gamma]: https://en.wikipedia.org/wiki/Inverse-gamma_distribution

[pdf]: https://en.wikipedia.org/wiki/Probability_density_function


  
    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][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> Evaluate the natural logarithm of the probability density function (PDF) for an [inverse gamma][inverse-gamma] distribution.

The [probability density function][pdf] (PDF) for an [inverse gamma][inverse-gamma] random variable is

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

`Installation`

``bash npm install @stdlib/stats-base-dists-invgamma-logpdf `

`Usage`

`javascript var logpdf = require( '@stdlib/stats-base-dists-invgamma-logpdf' ); `

#### logpdf( x, alpha, beta )

Evaluates the natural logarithm of the [probability density function][pdf] (PDF) for an [inverse gamma][inverse-gamma] distribution with parameters alpha (shape parameter) and beta (rate parameter).

`javascript var y = logpdf( 2.0, 0.5, 1.0 ); // returns ~-2.112

y = logpdf( 0.2, 1.0, 1.0 ); // returns ~-1.781

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

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

`javascript 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.

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

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

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

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

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

#### logpdf.factory( alpha, beta )

Returns a function for evaluating the natural logarithm of the [PDF][pdf] for an [inverse gamma][inverse-gamma] distribution with parameters alpha (shape parameter) and beta (rate parameter).

`javascript var mylogPDF = logpdf.factory( 6.0, 7.0 );

var y = mylogPDF( 2.0 ); // returns ~-1.464 `

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var logpdf = require( '@stdlib/stats-base-dists-invgamma-logpdf' );

var opts = { 'dtype': 'float64' }; var x = uniform( 10, 0.0, 2.0, opts ); var alpha = uniform( 10, 0.0, 5.0, opts ); var beta = uniform( 10, 0.0, 5.0, opts );

logEachMap( 'x: %0.4f, α: %0.4f, β: %0.4f, ln(f(x;α,β)): %0.4f', x, alpha, beta, logpdf ); `

*

`C APIs`

`$3`

`c #include "stdlib/stats/base/dists/invgamma/logpdf.h" `

#### stdlib_base_dists_invgamma_logpdf( alpha, beta )

Evaluates the natural logarithm of the probability density function (PDF) for an inverse gamma distribution with shape parameter alpha and scale parameter beta at a value x.

`c double out = stdlib_base_dists_invgamma_logpdf( 2.0, 0.5, 1.0 ); // returns ~-2.112 `

The function accepts the following arguments:

- x: [in] double input value. - alpha: [in] double shape parameter. - beta: [in] double scale parameter.

`c double stdlib_base_dists_invgamma_logpdf( const double x, const double mu, const double b ); `

`$3`

`c #include "stdlib/stats/base/dists/laplace/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 alpha; double beta; double x; double y; int i;

for ( i = 0; i < 25; i++ ) { x = random_uniform( 0.0, 10.0 ); alpha = random_uniform( 0.0, 10.0 ); beta = random_uniform( 0.0, 10.0 ); y = stdlib_base_dists_invgamma_logpdf( x, alpha, beta ); printf( "x: %lf, α: %lf, β: %lf, ln(f(x;α,β)): %lf\n", x, alpha, beta, y ); } } `

*

`Notice`

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`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-invgamma-logpdf.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-invgamma-logpdf

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-invgamma-logpdf/main/LICENSE

[inverse-gamma]: https://en.wikipedia.org/wiki/Inverse-gamma_distribution

[pdf]: https://en.wikipedia.org/wiki/Probability_density_function