Beta distribution cumulative distribution function (CDF).
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[Beta][beta-distribution] distribution [cumulative distribution function][cdf].
math
F(x;\alpha,\beta) = \frac{\mathop{\mathrm{Beta}}(x;\alpha,\beta)}{\mathop{\mathrm{Beta}}(\alpha,\beta)}alpha > 0 is the first shape parameter and beta > 0 is the second shape parameter. In the definition, Beta( x; a, b ) denotes the lower incomplete beta function and Beta( a, b ) the [beta function][beta-function].bash
npm install @stdlib/stats-base-dists-beta-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-beta-cdf' );alpha (first shape parameter) and beta (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 ~0.813
y = cdf( 0.2, 2.0, 2.0 );
// returns ~0.104
y = cdf( 0.8, 4.0, 4.0 );
// returns ~0.967
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 1.0NaN 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 NaNalpha <= 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 NaNbeta <= 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 NaNalpha (first shape parameter) and beta (second shape parameter).javascript
var mycdf = cdf.factory( 0.5, 0.5 );
var y = mycdf( 0.8 );
// returns ~0.705
y = mycdf( 0.3 );
// returns ~0.369javascript
var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var cdf = require( '@stdlib/stats-base-dists-beta-cdf' );
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 = cdf( x, alpha, beta );
console.log( 'x: %d, α: %d, β: %d, F(x;α,β): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}
