@stdlib/stats-base-dists-betaprime-logcdf
v0.2.2
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Evaluate the natural logarithm of the cumulative distribution function (CDF) for a beta prime distribution.
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Logarithm of Cumulative Distribution Function
Evaluate the natural logarithm of the cumulative distribution function for a beta prime distribution .
The cumulative distribution function for a beta prime random variable is
where alpha > 0
is the first shape parameter, beta > 0
is the second shape parameter and I
is the incomplete beta function.
Installation
npm install @stdlib/stats-base-dists-betaprime-logcdf
Usage
var logcdf = require( '@stdlib/stats-base-dists-betaprime-logcdf' );
logcdf( x, alpha, beta )
Evaluates the natural logarithm of the cumulative distribution function (CDF) for a beta prime distribution with parameters alpha
(first shape parameter) and beta
(second shape parameter).
var y = logcdf( 0.5, 1.0, 1.0 );
// returns ~-1.099
y = logcdf( 0.5, 2.0, 4.0 );
// returns ~-0.618
y = logcdf( 0.2, 2.0, 2.0 );
// returns ~-2.603
y = logcdf( 0.8, 4.0, 4.0 );
// returns ~-0.968
y = logcdf( -0.5, 4.0, 2.0 );
// returns -Infinity
y = logcdf( +Infinity, 4.0, 2.0 );
// returns 0.0
If provided NaN
as any argument, the function returns NaN
.
var y = logcdf( NaN, 1.0, 1.0 );
// returns NaN
y = logcdf( 0.0, NaN, 1.0 );
// returns NaN
y = logcdf( 0.0, 1.0, NaN );
// returns NaN
If provided alpha <= 0
, the function returns NaN
.
var y = logcdf( 2.0, -1.0, 0.5 );
// returns NaN
y = logcdf( 2.0, 0.0, 0.5 );
// returns NaN
If provided beta <= 0
, the function returns NaN
.
var y = logcdf( 2.0, 0.5, -1.0 );
// returns NaN
y = logcdf( 2.0, 0.5, 0.0 );
// returns NaN
logcdf.factory( alpha, beta )
Returns a function for evaluating the natural logarithm of the cumulative distribution function for a beta prime distribution with parameters alpha
(first shape parameter) and beta
(second shape parameter).
var mylogcdf = logcdf.factory( 0.5, 0.5 );
var y = mylogcdf( 0.8 );
// returns ~-0.767
y = mylogcdf( 0.3 );
// returns ~-1.143
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 EPS = require( '@stdlib/constants-float64-eps' );
var logcdf = require( '@stdlib/stats-base-dists-betaprime-logcdf' );
var alpha;
var beta;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
x = randu();
alpha = ( randu()*5.0 ) + EPS;
beta = ( randu()*5.0 ) + EPS;
y = logcdf( x, alpha, beta );
console.log( 'x: %d, α: %d, β: %d, ln(F(x;α,β)): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}
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.