npm package: @stdlib/stats-base-dists-signrank-pdf
Description: Wilcoxon signed rank test statistic probability density function (PDF).
Author: The Stdlib Authors
Latest version: 0.3.1

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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] -->

> Wilcoxon signed rank test statistic [probability density function][pdf].

<section class="intro">

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### pdf( x, n )

Evaluates the [probability density function][pdf] of the Wilcoxon signed rank test statistic with `n` observations.

```javascript
var y = pdf( 7.0, 9 );
// returns ~0.0098

y = pdf( 7.0, 6 );
// returns ~0.063

y = pdf( -1.0, 40 );
// returns 0.0
```

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

```javascript
var y = pdf( NaN, 8 );
// returns NaN

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

If provided `x < 0`, the function returns `NaN`.

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

If not provided a positive integer for `n`, the function returns `NaN`.

```javascript
var y = pdf( 2.0, 0 );
// returns NaN

y = pdf( 2.0, -2 );
// returns NaN

y = pdf( 2.0, 8.9 );
// returns NaN
```

#### pdf.factory( n )

Returns a function for evaluating the [probability density function][pdf] of the Wilcoxon signed rank test statistic with `n` observations.

```javascript
var mypdf = pdf.factory( 8 );
var y = mypdf( 4.0 );
// returns ~0.008

y = mypdf( 17.0 );
// returns ~0.051
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var ceil = require( '@stdlib/math-base-special-ceil' );
var randu = require( '@stdlib/random-base-randu' );
var pdf = require( '@stdlib/stats-base-dists-signrank-pdf' );

var n;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 30.0;
    n = ceil( randu() * 30.0 );
    y = pdf( x, n );
    console.log( 'x: %d, n: %d, f(x;n): %d', x.toFixed( 4 ), n.toFixed( 4 ), y.toFixed( 4 ) );
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

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<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

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

#### stdlib_base_dists_signrank_pdf( x, n )

Evaluates the probability density function (PDF) of the Wilcoxon signed rank test statistic with `n` observations.

```c
double out = stdlib_base_dists_signrank_pdf( 7.0, 9 );
// returns ~0.01
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.
-   **n**: `[in] int32_t` number of observations.

```c
double stdlib_base_dists_signrank_pdf( const double x, const int32_t n );
```

</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/signrank/pdf.h"
#include "stdlib/math/base/special/ceil.h"
#include <stdlib.h>
#include <stdio.h>
#include <stdint.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 ) {
    int32_t n;
    double x;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0, 30.0 );
        n = (int32_t)stdlib_base_ceil( random_uniform( 1.0, 30.0 ) );
        y = stdlib_base_dists_signrank_pdf( x, n );
        printf( "x: %lf, n: %d, f(x;n): %lf\n", x, n, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="related">

</section>

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

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