@stdlib/stats-base-dists-cosine-logpdf
v0.2.2
Published
Raised cosine distribution logarithm of probability density function (PDF).
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Logarithm of Probability Density Function
Raised cosine distribution logarithm of probability density function (PDF).
The probability density function (PDF) for a raised cosine random variable is
where μ
is the location parameter and s > 0
is the scale parameter.
Installation
npm install @stdlib/stats-base-dists-cosine-logpdf
Usage
var logpdf = require( '@stdlib/stats-base-dists-cosine-logpdf' );
logpdf( x, mu, s )
Evaluates the logarithm of the probability density function (PDF) for a raised cosine distribution with parameters mu
(location parameter) and s
(scale parameter).
var y = logpdf( 2.0, 0.0, 3.0 );
// returns ~-2.485
y = logpdf( -1.0, 2.0, 4.0 );
// returns ~-3.307
If provided NaN
as any argument, the function returns NaN
.
var y = logpdf( NaN, 0.0, 1.0 );
// returns NaN
y = logpdf( 0.0, NaN, 1.0 );
// returns NaN
y = logpdf( 0.0, 0.0, NaN );
// returns NaN
If provided s < 0
, the function returns NaN
.
var y = logpdf( 2.0, 0.0, -1.0 );
// returns NaN
If provided s = 0
, the function evaluates the logarithm of the PDF of a degenerate distribution centered at mu
.
var y = logpdf( 2.0, 8.0, 0.0 );
// returns -Infinity
y = logpdf( 8.0, 8.0, 0.0 );
// returns Infinity
logpdf.factory( mu, s )
Returns a function for evaluating the logarithm of the probability density function (PDF) of a raised cosine distribution with parameters mu
(location parameter) and s
(scale parameter).
var mylogpdf = logpdf.factory( 10.0, 2.0 );
var y = mylogpdf( 10.0 );
// returns ~-0.693
y = mylogpdf( 9.0 );
// returns ~-1.386
Notes
- In virtually all cases, using the
logpdf
orlogcdf
functions is preferable to manually computing the logarithm of thepdf
orcdf
, respectively, since the latter is prone to overflow and underflow.
Examples
var randu = require( '@stdlib/random-base-randu' );
var logpdf = require( '@stdlib/stats-base-dists-cosine-logpdf' );
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 = logpdf( x, mu, s );
console.log( 'x: %d, µ: %d, s: %d, ln(f(x;µ,s)): %d', x, mu, s, y );
}
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
License
See LICENSE.
Copyright
Copyright © 2016-2024. The Stdlib Authors.