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Cosine

Raised cosine distribution.

Installation

npm install @stdlib/stats-base-dists-cosine

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

var cosine = require( '@stdlib/stats-base-dists-cosine' );

cosine

Raised cosine distribution.

var dist = cosine;
// returns {...}

The namespace contains the following distribution functions:

• cdf( x, mu, s ): raised cosine distribution cumulative distribution function.
• logcdf( x, mu, s ): evaluate the natural logarithm of the cumulative distribution function (CDF) for a raised cosine distribution.
• logpdf( x, mu, s ): raised cosine distribution logarithm of probability density function (PDF).
• mgf( t, mu, s ): raised cosine distribution moment-generating function.
• pdf( x, mu, s ): raised cosine distribution probability density function (PDF).
• quantile( p, mu, s ): raised cosine distribution quantile function.

The namespace contains the following functions for calculating distribution properties:

• kurtosis( mu, s ): raised cosine distribution excess kurtosis.
• mean( mu, s ): raised cosine distribution expected value.
• median( mu, s ): raised cosine distribution median.
• mode( mu, s ): raised cosine distribution mode.
• skewness( mu, s ): raised cosine distribution skewness.
• stdev( mu, s ): raised cosine distribution standard deviation.
• variance( mu, s ): raised cosine distribution variance.

The namespace contains a constructor function for creating a raised cosine distribution object.

• Cosine( [mu, s] ): raised cosine distribution constructor.

var Cosine = require( '@stdlib/stats-base-dists-cosine' ).Cosine;

var dist = new Cosine( 2.0, 4.0 );

var y = dist.cdf( 0.5 );
// returns ~0.165

Examples

var cosine = require( '@stdlib/stats-base-dists-cosine' );

// Create a raised cosine distribution:
var mu = 2.0;
var s = 1.5;
var dist = new cosine.Cosine( mu, s );

// Calculate various distribution properties:
console.log( 'Mean: %d', dist.mean );
// => 'Mean: 2'

console.log( 'Median: %d', dist.median );
// => 'Median: 2'

console.log( 'Mode: %d', dist.mode );
// => 'Mode: 2'

console.log( 'Standard Deviation: %d', dist.stdev );
// => 'Standard Deviation: 0.5422680827869919'

console.log( 'Variance: %d', dist.variance );
// => 'Variance: 0.29405467360947996'

// Evaluate the probability density function (PDF):
var x = 1.5;
console.log( 'PDF( %d ): %d', x, dist.pdf( x ) );
// => 'PDF( 1.5 ): 0.5'

// Evaluate the cumulative distribution function (CDF):
console.log( 'CDF( %d ): %d', x, dist.cdf( x ) );
// => 'CDF( 1.5 ): 0.19550110947788535'

// Calculate distribution moments:
console.log( 'Skewness: %d', cosine.skewness( mu, s ) );
// => 'Skewness: 0'

console.log( 'Excess Kurtosis: %d', cosine.kurtosis( mu, s ) );
// => 'Excess Kurtosis: -0.5937628755982807'

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Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.