@stdlib/stats-base-dists-cosine-logcdf
v0.2.2
Published
Natural logarithm of cumulative distribution function (CDF) for a raised cosine distribution.
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Logarithm of Cumulative Distribution Function
Evaluate the natural logarithm of the cumulative distribution function (CDF) for a raised cosine distribution.
The cumulative distribution function 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-logcdf
Usage
var logcdf = require( '@stdlib/stats-base-dists-cosine-logcdf' );
logcdf( x, mu, s )
Evaluates the natural logarithm of the cumulative distribution function (CDF) for a raised cosine distribution with parameters mu
(location parameter) and s
(scale parameter).
var y = logcdf( 2.0, 0.0, 3.0 );
// returns ~-0.029
y = logcdf( 0.0, 0.0, 1.0 );
// returns ~-0.693
y = logcdf( -1.0, 4.0, 2.0 );
// returns -Infinity
If provided NaN
as any argument, the function returns NaN
.
var y = logcdf( NaN, 0.0, 1.0 );
// returns NaN
y = logcdf( 0.0, NaN, 1.0 );
// returns NaN
y = logcdf( 0.0, 0.0, NaN );
// returns NaN
If provided s < 0
, the function returns NaN
.
var y = logcdf( 2.0, 0.0, -1.0 );
// returns NaN
If provided s = 0
, the function evaluates the logarithm of the CDF for a degenerate distribution centered at mu
.
var y = logcdf( 2.0, 8.0, 0.0 );
// returns -Infinity
y = logcdf( 8.0, 8.0, 0.0 );
// returns 0.0
y = logcdf( 10.0, 8.0, 0.0 );
// returns 0.0
logcdf.factory( mu, s )
Returns a function for evaluating the natural logarithm of the cumulative distribution function of a raised cosine distribution with parameters mu
(location parameter) and s
(scale parameter).
var mylogcdf = logcdf.factory( 10.0, 2.0 );
var y = mylogcdf( 10.0 );
// returns ~-0.693
y = mylogcdf( 8.0 );
// returns -Infinity
y = mylogcdf( 12.0 );
// returns 0.0
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 logcdf = require( '@stdlib/stats-base-dists-cosine-logcdf' );
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 = logcdf( 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.