https://github.com/stdlib-js/stats-base-dists-cosine-logcdf
Natural logarithm of cumulative distribution function (CDF) for a raised cosine distribution.
https://github.com/stdlib-js/stats-base-dists-cosine-logcdf
cdf continuous cosine cumulative-distribution dist distribution distribution-function javascript ln log logarithm natural node node-js nodejs probability statistics stats stdlib univariate
Last synced: 23 days ago
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Natural logarithm of cumulative distribution function (CDF) for a raised cosine distribution.
- Host: GitHub
- URL: https://github.com/stdlib-js/stats-base-dists-cosine-logcdf
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:08:57.000Z (over 4 years ago)
- Default Branch: main
- Last Pushed: 2025-11-21T22:50:36.000Z (2 months ago)
- Last Synced: 2025-11-22T00:20:33.567Z (2 months ago)
- Topics: cdf, continuous, cosine, cumulative-distribution, dist, distribution, distribution-function, javascript, ln, log, logarithm, natural, node, node-js, nodejs, probability, statistics, stats, stdlib, univariate
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 986 KB
- Stars: 2
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
- Notice: NOTICE
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README
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# Logarithm of Cumulative Distribution 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 [cumulative distribution function][cdf] (CDF) for a [raised cosine][cosine-distribution] distribution.
The [cumulative distribution function][cdf] for a [raised cosine][cosine-distribution] random variable is
```math
F(x;\mu ,s)=\begin{cases} 0 & \text{ for } x < \mu - s \\ {\frac {1}{2}}\left[1\!+\!{\frac {x\!-\!\mu }{s}}\!+\!{\frac {1}{\pi }}\sin \left({\frac {x\!-\!\mu }{s}}\,\pi \right)\right] & \text{ for } \mu - s \le x \le \mu + s \\ 1 & \text{ for } x > \mu + s \end{cases}
```
where `μ` is the location parameter and `s > 0` is the scale parameter.
## Installation
```bash
npm install @stdlib/stats-base-dists-cosine-logcdf
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## Usage
```javascript
var logcdf = require( '@stdlib/stats-base-dists-cosine-logcdf' );
```
#### logcdf( x, mu, s )
Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [raised cosine][cosine-distribution] distribution with parameters `mu` (location parameter) and `s` (scale parameter).
```javascript
var y = logcdf( 2.0, 0.0, 3.0 );
// returns ~-0.029
y = logcdf( 0.0, 0.0, 1.0 );
// returns ~-0.693
y = logcdf( -1.0, 4.0, 2.0 );
// returns -Infinity
```
If provided `NaN` as any argument, the function returns `NaN`.
```javascript
var y = logcdf( NaN, 0.0, 1.0 );
// returns NaN
y = logcdf( 0.0, NaN, 1.0 );
// returns NaN
y = logcdf( 0.0, 0.0, NaN );
// returns NaN
```
If provided `s < 0`, the function returns `NaN`.
```javascript
var y = logcdf( 2.0, 0.0, -1.0 );
// returns NaN
```
If provided `s = 0`, the function evaluates the logarithm of the [CDF][cdf] for a [degenerate distribution][degenerate-distribution] centered at `mu`.
```javascript
var y = logcdf( 2.0, 8.0, 0.0 );
// returns -Infinity
y = logcdf( 8.0, 8.0, 0.0 );
// returns 0.0
y = logcdf( 10.0, 8.0, 0.0 );
// returns 0.0
```
#### logcdf.factory( mu, s )
Returns a function for evaluating the natural logarithm of the [cumulative distribution function][cdf] of a [raised cosine][cosine-distribution] distribution with parameters `mu` (location parameter) and `s` (scale parameter).
```javascript
var mylogcdf = logcdf.factory( 10.0, 2.0 );
var y = mylogcdf( 10.0 );
// returns ~-0.693
y = mylogcdf( 8.0 );
// returns -Infinity
y = mylogcdf( 12.0 );
// returns 0.0
```
## 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
```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var logcdf = require( '@stdlib/stats-base-dists-cosine-logcdf' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 10, 0.0, 10.0, opts );
var mu = uniform( 10, 0.0, 10.0, opts );
var s = uniform( 10, 0.0, 10.0, opts );
logEachMap( 'x: %0.4f, µ: %0.4f, s: %0.4f, ln(F(x;µ,s)): %0.4f', x, mu, s, logcdf );
```
* * *
## C APIs
### Usage
```c
#include "stdlib/stats/base/dists/cosine/logcdf.h"
```
#### stdlib_base_dists_cosine_logcdf( x, mu, s )
Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [raised cosine][cosine-distribution] distribution with parameters `mu` (location parameter) and `s` (scale parameter).
```c
double out = stdlib_base_dists_cosine_logcdf( 0.5, 0.0, 1.0 );
// returns ~0.909
```
The function accepts the following arguments:
- **x**: `[in] double` input value.
- **mu**: `[in] double` location parameter.
- **s**: `[in] double` scale parameter.
```c
double stdlib_base_dists_cosine_logcdf( const double x, const double mu, const double s );
```
### Examples
```c
#include "stdlib/stats/base/dists/cosine/cdf.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 mu;
double s;
double x;
double y;
int i;
for ( i = 0; i < 10; i++ ) {
x = random_uniform( -50.0, 50.0 );
mu = random_uniform( -50.0, 50.0 );
s = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
y = stdlib_base_dists_cosine_logcdf( x, mu, s );
printf( "x: %lf, µ: %lf, s: %lf, ln(F(x;µ,s)): %lf\n", x, mu, s, y );
}
return 0;
}
```
* * *
## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].
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[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-cosine-logcdf
[test-image]: https://github.com/stdlib-js/stats-base-dists-cosine-logcdf/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/stats-base-dists-cosine-logcdf/actions/workflows/test.yml?query=branch:main
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[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-cosine-logcdf?branch=main
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[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-cosine-logcdf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-cosine-logcdf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-cosine-logcdf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-cosine-logcdf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-cosine-logcdf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-cosine-logcdf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-cosine-logcdf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-cosine-logcdf/main/LICENSE
[cosine-distribution]: https://en.wikipedia.org/wiki/Raised_cosine_distribution
[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution