Arcsine distribution cumulative distribution function (CDF).
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[Arcsine][arcsine-distribution] distribution [cumulative distribution function][cdf].
math
F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)a is the minimum support and b is the maximum support. The parameters must satisfy a < b.bash
npm install @stdlib/stats-base-dists-arcsine-cdfscript tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var cdf = require( '@stdlib/stats-base-dists-arcsine-cdf' );a (minimum support) and b (maximum support).javascript
var y = cdf( 9.0, 0.0, 10.0 );
// returns ~0.795
y = cdf( 0.5, 0.0, 2.0 );
// returns ~0.333
y = cdf( -Infinity, 2.0, 4.0 );
// returns 0.0
y = cdf( +Infinity, 2.0, 4.0 );
// returns 1.0NaN as any argument, the function returns NaN.javascript
var y = cdf( NaN, 0.0, 1.0 );
// returns NaN
y = cdf( 0.0, NaN, 1.0 );
// returns NaN
y = cdf( 0.0, 0.0, NaN );
// returns NaNa >= b, the function returns NaN.javascript
var y = cdf( 1.0, 2.5, 2.0 );
// returns NaNa (minimum support) and b (maximum support).javascript
var mycdf = cdf.factory( 0.0, 10.0 );
var y = mycdf( 0.5 );
// returns ~0.144
y = mycdf( 8.0 );
// returns ~0.705javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdf = require( '@stdlib/stats-base-dists-arcsine-cdf' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 25, -10.0, 10.0, opts );
var a = uniform( x.length, -20.0, 0.0, opts );
var b = uniform( x.length, 0.0, 40.0, opts );
logEachMap( 'x: %0.4f, a: %0.4f, b: %0.4f, F(x;a,b): %0.4f', x, a, b, cdf );c
#include "stdlib/stats/base/dists/arcsine/cdf.h"c
double out = stdlib_base_dists_arcsine_cdf( 0.5, 0.0, 2.0 );
// returns ~0.333[in] double input value.[in] double minimum support.[in] double maximum support.c
double stdlib_base_dists_arcsine_cdf( const double x, const double a, const double b );c
#include "stdlib/stats/base/dists/arcsine/cdf.h"
#include <stdlib.h>
#include <stdio.h>
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( -10.0, 10.0 );
a = random_uniform( -20.0, 0.0 );
b = random_uniform( a, a+40.0 );
y = stdlib_base_dists_arcsine_cdf( x, a, b );
printf( "x: %lf, a: %lf, b: %lf, F(x;a,b): %lf\n", x, a, b, y );
}
}
