@stdlib/stats-base-dists-cosine-cdf
v0.3.1TypeScript
Raised cosine distribution cumulative distribution function (CDF).
stdlibstdmathstatisticsstatsdistributiondistprobabilitycdfcumulative distributiondistribution function
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Published by The Stdlib Authors
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Cumulative Distribution Function
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> [Raised cosine][cosine-distribution] distribution [cumulative distribution function][cdf].
The [cumulative distribution function][cdf] for a [raised cosine][cosine-distribution] random variable is
where μ is the location parameter and s > 0 is the scale parameter.
Installation
``bash`
npm install @stdlib/stats-base-dists-cosine-cdf
Usage
`javascript`
var cdf = require( '@stdlib/stats-base-dists-cosine-cdf' );
#### cdf( x, mu, s )
Evaluates 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 = cdf( 2.0, 0.0, 3.0 );
// returns ~0.971
y = cdf( 0.0, 0.0, 1.0 );
// returns ~0.5
y = cdf( -1.0, 4.0, 2.0 );
// returns 0.0
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = cdf( NaN, 0.0, 1.0 );
// returns NaN
y = cdf( 0.0, NaN, 1.0 );
// returns NaN
y = cdf( 0.0, 0.0, NaN );
// returns NaN
`
If provided s < 0, the function returns NaN.
`javascript`
var y = cdf( 2.0, 0.0, -1.0 );
// returns NaN
If provided s = 0, the function evaluates the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at mu.
`javascript
var y = cdf( 2.0, 8.0, 0.0 );
// returns 0.0
y = cdf( 8.0, 8.0, 0.0 );
// returns 1.0
y = cdf( 10.0, 8.0, 0.0 );
// returns 1.0
`
#### cdf.factory( mu, s )
Returns a function for evaluating the [cumulative distribution function][cdf] of a [raised cosine][cosine-distribution] distribution with parameters mu (location parameter) and s (scale parameter).
`javascript
var mycdf = cdf.factory( 10.0, 2.0 );
var y = mycdf( 10.0 );
// returns 0.5
y = mycdf( 8.0 );
// returns 0.0
y = mycdf( 12.0 );
// returns 1.0
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdf = require( '@stdlib/stats-base-dists-cosine-cdf' );
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, F(x;µ,s): %0.4f', x, mu, s, cdf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/cosine/cdf.h"
#### stdlib_base_dists_cosine_cdf( x, mu, s )
Evaluates 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_cdf( 0.5, 0.0, 1.0 );
// returns ~0.909
The function accepts the following arguments:
- x: [in] double input value.[in] double
- mu: location parameter.[in] double
- s: scale parameter.
`c`
double stdlib_base_dists_cosine_cdf( const double x, const double mu, const double s );
$3
`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( -100.0, 0.0 );
mu = random_uniform( -50.0, 50.0 );
s = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
y = stdlib_base_dists_cosine_cdf( x, mu, s );
printf( "x: %lf, µ: %lf, s: %lf, 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 © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[deno-readme]: https://github.com/stdlib-js/stats-base-dists-cosine-cdf/blob/deno/README.md
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[esm-url]: https://github.com/stdlib-js/stats-base-dists-cosine-cdf/tree/esm
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-cosine-cdf/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