@stdlib/stats-base-dists-weibull-logcdf
v0.2.2
Published
Weibull distribution logarithm of cumulative distribution function (CDF).
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Logarithm of Cumulative Distribution Function
Weibull distribution logarithm of cumulative distribution function.
The cumulative distribution function for a Weibull random variable is
where lambda > 0
is the shape parameter and k > 0
is the scale parameter.
Installation
npm install @stdlib/stats-base-dists-weibull-logcdf
Usage
var logcdf = require( '@stdlib/stats-base-dists-weibull-logcdf' );
logcdf( x, k, lambda )
Evaluates the natural logarithm of the cumulative distribution function (CDF) for a Weibull distribution with shape parameter k
and scale parameter lambda
.
var y = logcdf( 2.0, 1.0, 0.5 );
// returns ~-0.018
y = logcdf( 0.0, 0.5, 1.0 );
// returns -Infinity
y = logcdf( -Infinity, 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 k <= 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 lambda <= 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( k, lambda )
Returns a function for evaluating the cumulative distribution function of a Weibull distribution with shape parameter k
and scale parameter lambda
.
var mylogcdf = logcdf.factory( 2.0, 10.0 );
var y = mylogcdf( 10.0 );
// returns ~-0.459
y = mylogcdf( 8.0 );
// returns ~-0.749
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-weibull-logcdf' );
var lambda;
var k;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
x = randu() * 10.0;
lambda = randu() * 10.0;
k = randu() * 10.0;
y = logcdf( x, lambda, k );
console.log( 'x: %d, k: %d, λ: %d, ln(F(x;k,λ)): %d', x, k, lambda, 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.