Cosine

Raised cosine distribution.

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'