@stdlib/stats-base-dists-kumaraswamy-cdf
v0.3.1TypeScript
Kumaraswamy's double bounded distribution cumulative distribution function (CDF).
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Cumulative Distribution Function
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> [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution [cumulative distribution function][cdf].
The [cumulative distribution function][cdf] 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-cdf
Usage
`javascript`
var cdf = require( '@stdlib/stats-base-dists-kumaraswamy-cdf' );
#### cdf( x, a, b )
Evaluates the [cumulative distribution function][cdf] (CDF) for a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution with parameters a (first shape parameter) and b (second shape parameter).
`javascript
var y = cdf( 0.5, 1.0, 1.0 );
// returns 0.5
y = cdf( 0.5, 2.0, 4.0 );
// returns ~0.684
y = cdf( 0.2, 2.0, 2.0 );
// returns ~0.078
y = cdf( 0.8, 4.0, 4.0 );
// returns ~0.878
y = cdf( -0.5, 4.0, 2.0 );
// returns 0.0
y = cdf( -Infinity, 4.0, 2.0 );
// returns 0.0
y = cdf( 1.5, 4.0, 2.0 );
// returns 1.0
y = cdf( +Infinity, 4.0, 2.0 );
// returns 1.0
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = cdf( NaN, 1.0, 1.0 );
// returns NaN
y = cdf( 0.0, NaN, 1.0 );
// returns NaN
y = cdf( 0.0, 1.0, NaN );
// returns NaN
`
If provided a <= 0, the function returns NaN.
`javascript
var y = cdf( 2.0, -1.0, 0.5 );
// returns NaN
y = cdf( 2.0, 0.0, 0.5 );
// returns NaN
`
If provided b <= 0, the function returns NaN.
`javascript
var y = cdf( 2.0, 0.5, -1.0 );
// returns NaN
y = cdf( 2.0, 0.5, 0.0 );
// returns NaN
`
#### cdf.factory( a, b )
Returns a function for evaluating the [cumulative distribution function][cdf] for a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution with parameters a (first shape parameter) and b (second shape parameter).
`javascript
var mycdf = cdf.factory( 0.5, 0.5 );
var y = mycdf( 0.8 );
// returns ~0.675
y = mycdf( 0.3 );
// returns ~0.327
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var EPS = require( '@stdlib/constants-float64-eps' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdf = require( '@stdlib/stats-base-dists-kumaraswamy-cdf' );
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, F(x;a,b): %0.4f', x, a, b, cdf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/kumaraswamy/cdf.h"
#### stdlib_base_dists_kumaraswamy_cdf( x, a, b )
Evaluates the [cumulative distribution function][cdf] (CDF) for a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution with parameters a (first shape parameter) and b (second shape parameter).
`c`
double out = stdlib_base_dists_kumaraswamy_cdf( 0.5, 1.0, 1.0 );
// returns 0.5
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_cdf( const double x, const double a, const double b );
$3
`c
#include "stdlib/stats/base/dists/kumaraswamy/cdf.h"
#include "stdlib/constants/float64/eps.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( 0.0, 1.0 );
a = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );
b = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );
y = stdlib_base_dists_kumaraswamy_cdf( x, a, b );
printf( "x: %lf, a: %lf, b: %lf, 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].
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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
[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function