Probability Density Function

Raised cosine distribution probability density function (PDF).

The probability density function (PDF) for a raised cosine random variable is

f left-parenthesis x semicolon mu comma s right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column StartFraction 1 Over 2 s EndFraction left-bracket 1 plus cosine left-parenthesis StartFraction x minus mu Over s EndFraction pi right-parenthesis right-bracket 2nd Column for mu minus s less-than-or-equal-to x less-than-or-equal-to mu plus s 2nd Row 1st Column 0 2nd Column otherwise EndLayout

where μ is the location parameter and s > 0 is the scale parameter.

Usage

var pdf = require( '@stdlib/math/base/dists/cosine/pdf' );

pdf( x, mu, s )

Evaluates the probability density function (PDF) for a raised cosine distribution with parameters mu (location parameter) and s (scale parameter).

var y = pdf( 2.0, 0.0, 3.0 );
// returns ~0.083

y = pdf( 2.0, 4.0, 4.0 );
// returns ~0.125

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

var y = pdf( NaN, 0.0, 1.0 );
// returns NaN

y = pdf( 0.0, NaN, 1.0 );
// returns NaN

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

If provided s < 0, the function returns NaN.

var y = pdf( 2.0, 0.0, -1.0 );
// returns NaN

If provided s = 0, the function evaluates the PDF of a degenerate distribution centered at mu.

var y = pdf( 2.0, 8.0, 0.0 );
// returns 0.0

y = pdf( 8.0, 8.0, 0.0 );
// returns Infinity

pdf.factory( mu, s )

Returns a function for evaluating the probability density function (PDF) of a raised cosine distribution with parameters mu (location parameter) and s (scale parameter).

var mypdf = pdf.factory( 0.0, 3.0 );

var y = mypdf( 2.0 );
// returns ~0.083

y = mypdf( 5.0 );
// returns 0.0

Examples

var randu = require( '@stdlib/random/base/randu' );
var pdf = require( '@stdlib/math/base/dists/cosine/pdf' );

var mu;
var s;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    mu = randu() * 10.0;
    s = randu() * 10.0;
    y = pdf( x, mu, s );
    console.log( 'x: %d, µ: %d, s: %d, f(x;µ,s): %d', x, mu, s, y );
}