npm package: @stdlib/stats-base-dists-bradford-pdf
Description: Bradford distribution probability density function (PDF).
Author: The Stdlib Authors
Latest version: 0.1.1

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# 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] -->

> [Bradford][bradford-distribution] distribution [probability density function][pdf] (PDF).

<section class="intro">

The [probability density function][pdf] (PDF) for a [Bradford][bradford-distribution] random variable is

<!-- <equation class="equation" label="eq:bradford_pdf" align="center" raw="f(x;c)=\frac{c}{(\ln(1+c)) (1 + cx)}" alt="Probability density function (PDF) for a Bradford distribution."> -->

<div class="equation" align="center" data-raw-text="f(x;c)=\frac{c}{(\ln(1+c)) (1 + cx)}" data-equation="eq:bradford_pdf">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/bradford/pdf/docs/img/equation_bradford_pdf.svg" alt="Probability density function (PDF) for a Bradford distribution.">
    <br>
</div>

<!-- </equation> -->

where `c > 0` is the shape parameter of the distribution.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-bradford-pdf
```

</section>

<section class="usage">

## Usage

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

#### pdf( x, c )

Evaluates the [probability density function][pdf] (PDF) for a [Bradford][bradford-distribution] distribution with shape parameter `c` at a value `x`.

```javascript
var y = pdf( 0.1, 0.1 );
// returns ~1.039

y = pdf( 0.5, 5.0 );
// returns ~0.797

y = pdf( 1.0, 10.0 );
// returns ~0.379
```

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

```javascript
var y = pdf( NaN, 1.0 );
// returns NaN

y = pdf( 0.0, NaN );
// returns NaN
```

If provided an `x` value which is outside the support `[0,1]`, the function returns `0`.

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

y = pdf( -0.5, 1.0 );
// returns 0.0
```

If provided a shape parameter `c <= 0`, the function returns `NaN`.

```javascript
var y = pdf( 0.5, 0.0 );
// returns NaN

y = pdf( 0.5, -5.0 );
// returns NaN
```

#### pdf.factory( c )

Returns a function for evaluating the [PDF][pdf] of a [Bradford][bradford-distribution] distribution with shape parameter `c`.

```javascript
var myPDF = pdf.factory( 5.0 );
var y = myPDF( 0.5 );
// returns ~0.797

y = myPDF( 1.0 );
// returns ~0.465
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

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

var opts = {
    'dtype': 'float64'
};
var c = uniform( 10, 0.0, 1.0, opts );
var x = uniform( 10, 0.1, 10.0, opts );

logEachMap( 'x: %0.4f, c: %0.4f, f(x;c): %0.4f', x, c, pdf );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

<section class="c">

## C APIs

<section class="intro">

</section>

<!-- /.intro -->

<section class="usage">

### Usage

```c
#include "stdlib/stats/base/dists/bradford/pdf.h"
```

#### stdlib_base_dists_bradford_pdf( x, c )

Evaluates the probability density function for a Bradford distribution.

```c
double out = stdlib_base_dists_bradford_pdf( 0.5, 5.0 );
// returns ~0.797
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.
-   **c**: `[in] double` shape parameter.

```c
double stdlib_base_dists_bradford_pdf( const double x, const double c );
```

</section>

<!-- /.usage -->

<section class="notes">

</section>

<!-- /.notes -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/bradford/pdf.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 x;
    double c;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        x = random_uniform( 0.0, 1.0 );
        c = random_uniform( 0.01, 10.0 );
        y = stdlib_base_dists_bradford_pdf( x, c );
        printf( "x: %lf, c: %lf, f(x;c): %lf\n", x, c, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<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

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

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

</section>

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

[bradford-distribution]: https://en.wikipedia.org/wiki/Bradford%27s_law

</section>

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