@stdlib/stats-base-dists-kumaraswamy-logpdf
v0.3.1TypeScript
Natural logarithm of the probability density function (PDF) for a Kumaraswamy's double bounded distribution.
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Logarithm of Probability Density Function
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> Evaluate the natural logarithm of the [probability density function][pdf] for a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution.
The [probability density function][pdf] (PDF) for a [Kumaraswamy's double bounded][kumaraswamy-distribution] random variable is
where a > 0 is the first shape parameter and b > 0 is the second shape parameter.
Installation
``bash`
npm install @stdlib/stats-base-dists-kumaraswamy-logpdf
Usage
`javascript`
var logpdf = require( '@stdlib/stats-base-dists-kumaraswamy-logpdf' );
#### logpdf( x, a, b )
Evaluates the natural logarithm of the [probability density function][pdf] (PDF) for a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution with parameters a (first shape parameter) and b (second shape parameter).
`javascript
var y = logpdf( 0.5, 1.0, 1.0 );
// returns 0.0
y = logpdf( 0.5, 2.0, 4.0 );
// returns ~0.523
y = logpdf( 0.2, 2.0, 2.0 );
// returns ~-0.264
y = logpdf( 0.8, 4.0, 4.0 );
// returns ~0.522
y = logpdf( -0.5, 4.0, 2.0 );
// returns -Infinity
y = logpdf( -Infinity, 4.0, 2.0 );
// returns -Infinity
y = logpdf( 1.5, 4.0, 2.0 );
// returns -Infinity
y = logpdf( +Infinity, 4.0, 2.0 );
// returns -Infinity
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = logpdf( NaN, 1.0, 1.0 );
// returns NaN
y = logpdf( 0.0, NaN, 1.0 );
// returns NaN
y = logpdf( 0.0, 1.0, NaN );
// returns NaN
`
If provided a <= 0, the function returns NaN.
`javascript
var y = logpdf( 2.0, -1.0, 0.5 );
// returns NaN
y = logpdf( 2.0, 0.0, 0.5 );
// returns NaN
`
If provided b <= 0, the function returns NaN.
`javascript
var y = logpdf( 2.0, 0.5, -1.0 );
// returns NaN
y = logpdf( 2.0, 0.5, 0.0 );
// returns NaN
`
#### logpdf.factory( a, b )
Returns a function for evaluating the natural logarithm of the [probability density function][pdf] (PDF) for a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution with parameters a (first shape parameter) and b (second shape parameter).
`javascript
var mylogpdf = logpdf.factory( 0.5, 0.5 );
var y = mylogpdf( 0.8 );
// returns ~-0.151
y = mylogpdf( 0.3 );
// returns ~-0.388
`
Notes
- In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.
Examples
`javascript
var EPS = require( '@stdlib/constants-float64-eps' );
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var logpdf = require( '@stdlib/stats-base-dists-kumaraswamy-logpdf' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 10, 0.0, 1.0, opts );
var a = uniform( 10, EPS, 5.0, opts );
var b = uniform( 10, EPS, 5.0, opts );
logEachMap( 'x: %0.4f, a: %0.4f, b: %0.4f, ln(f(x;a,b)): %0.4f', x, a, b, logpdf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/kumaraswamy/logpdf.h"
#### stdlib_base_dists_kumaraswamy_logpdf( x, a, b )
Evaluates the natural logarithm of the probability distribution function (PDF) for a Kumaraswamy's double bounded distribution.
`c`
double out = stdlib_base_dists_kumaraswamy_logpdf( 0.5, 1.0, 1.0 );
// returns 0.0
The function accepts the following arguments:
- x: [in] double input value.[in] double
- a: first shape parameter.[in] double
- b: second shape parameter.
`c`
double stdlib_base_dists_kumaraswamy_logpdf( const double x, const double a, const double b );
$3
`c
#include "stdlib/stats/base/dists/kumaraswamy/logpdf.h"
#include
#include
static double random_uniform( const double min, const double max ) {
double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
return min + ( v*(max-min) );
}
int main( void ) {
double x;
double a;
double b;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
x = random_uniform( 0, 1.0 );
a = random_uniform( 0, 5.0 );
b = random_uniform( 0, 5.0 );
y = stdlib_base_dists_kumaraswamy_logpdf( x, a, b );
printf( "x: %lf, a: %lf, b: %lf, ln(f(x;a,b)): %lf\n", x, a, b, y );
}
}
`
*
Notice
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
#### Community
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---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[kumaraswamy-distribution]: https://en.wikipedia.org/wiki/Kumaraswamy_distribution
[pdf]: https://en.wikipedia.org/wiki/Probability_density_function