npm package: @stdlib/stats-base-dists-degenerate-logpdf
Description: Degenerate distribution logarithm of probability density function (logPDF).
Author: The Stdlib Authors
Latest version: 0.3.1

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# Logarithm of Probability Density Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> [Degenerate distribution][degenerate-distribution] logarithm of [probability density function][pdf] (logPDF).

<section class="intro">

Strictly speaking, as a discrete distribution, a [degenerate][degenerate-distribution] has no [probability density function][pdf] (PDF). Extending the notion of a [PDF][pdf], we conceptualize the [PDF][pdf] of a [degenerate][degenerate-distribution] distribution as an infinitely tall spike centered at `mu`. More formally,

<!-- <equation class="equation" label="eq:degenerate_pdf" align="center" raw="f(x;\mu) = \delta(x-\mu)" alt="Probability density function (PDF) for a degenerate distribution."> -->

<div class="equation" align="center" data-raw-text="f(x;\mu) = \delta(x-\mu)" data-equation="eq:degenerate_pdf">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/degenerate/logpdf/docs/img/equation_degenerate_pdf.svg" alt="Probability density function (PDF) for a degenerate distribution.">
    <br>
</div> -->

<!-- </equation> -->

where `delta` is the Dirac delta function.

<!-- <equation class="equation" label="eq:dirac_delta" align="center" raw="\delta(x) = {\begin{cases}+\infty , & x = 0\\0, & x \neq 0\end{cases}}" alt="Dirac delta function."> -->

<!-- <div class="equation" align="center" data-raw-text="\delta(x) = {\begin{cases}+\infty , &amp; x = 0\\0, &amp; x \neq 0\end{cases}}" data-equation="eq:dirac_delta">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/degenerate/logpdf/docs/img/equation_dirac_delta.svg" alt="Dirac delta function.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### logpdf( x, mu )

Evaluates the natural logarithm of the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.

```javascript
var y = logpdf( 2.0, 8.0 );
// returns -Infinity

y = logpdf( 8.0, 8.0 );
// returns Infinity
```

#### logpdf.factory( mu )

Returns a function for evaluating the natural logarithm of the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.

```javascript
var mylogpdf = logpdf.factory( 10.0 );

var y = mylogpdf( 10.0 );
// returns Infinity

y = mylogpdf( 5.0 );
// returns -Infinity

y = mylogpdf( 12.0 );
// returns -Infinity
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

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

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 100, 0, 5, opts );
var mu = discreteUniform( 100, 0, 5, opts );

logEachMap( 'x: %d, µ: %d, ln(f(x;µ)): %0.4f', x, mu, logpdf );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

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

#### stdlib_base_dists_degenerate_logpdf( x, mu )

Evaluates the natural logarithm of the probability density function (logPDF) for a degenerate distribution.

```c
double out = stdlib_base_dists_degenerate_logpdf( 2.0, 3.0 );
// returns -Infinity
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.
-   **mu**: `[in] double` constant value of the distribution.

```c
double stdlib_base_dists_degenerate_logpdf( const double x, const double mu );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/degenerate/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 mu;
    double x;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0.0, 5.0 );
        mu = random_uniform( 0.0, 5.0 );
        y = stdlib_base_dists_degenerate_logpdf( x, mu );
        printf( "x: %lf, µ: %lf, ln(f(x;µ)): %lf\n", x, mu, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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

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

[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution

</section>

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