stdlib-js
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About stdlib...
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Cumulative Distribution Function
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[Gamma][gamma-distribution] distribution [cumulative distribution function][cdf].
alpha is the shape parameter and beta is the rate parameter of the distribution. gamma is the lower [incomplete gamma function][@stdlib/math/base/special/gammainc].
bash
npm install @stdlib/stats-base-dists-gamma-cdf
javascript
var cdf = require( '@stdlib/stats-base-dists-gamma-cdf' );
#### cdf( x, alpha, beta )
Evaluates the [cumulative distribution function][cdf] (CDF) for a [gamma][gamma-distribution] distribution with parameters alpha (shape parameter) and beta (rate parameter).
javascript
var y = cdf( 2.0, 1.0, 1.0 );
// returns ~0.865
y = cdf( 2.0, 3.0, 1.0 );
// returns ~0.323
y = cdf( -1.0, 2.0, 2.0 );
// returns 0.0
y = cdf( -Infinity, 4.0, 2.0 );
// returns 0.0
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 alpha < 0, the function returns NaN.
javascript
var y = cdf( 2.0, -1.0, 0.5 );
// returns NaN
If provided alpha = 0, the function evaluates the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at 0.
javascript
var y = cdf( 2.0, 0.0, 2.0 );
// returns 1.0
y = cdf( -2.0, 0.0, 2.0 );
// returns 0.0
y = cdf( 0.0, 0.0, 2.0 );
// returns 1.0
If provided beta <= 0, the function returns NaN.
javascript
var y = cdf( 2.0, 0.5, -1.0 );
// returns NaN
#### cdf.factory( alpha, beta )
Returns a function for evaluating the [cumulative distribution function][cdf] for a [gamma][gamma-distribution] distribution with parameters alpha (shape parameter) and beta (rate parameter).
javascript
var mycdf = cdf.factory( 0.5, 0.1 );
var y = mycdf( 12.0 );
// returns ~0.879
y = mycdf( 8.0 );
// returns ~0.794
javascript
var randu = require( '@stdlib/random-base-randu' );
var cdf = require( '@stdlib/stats-base-dists-gamma-cdf' );
var alpha;
var beta;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
x = randu() * 3.0;
alpha = randu() * 5.0;
beta = randu() * 5.0;
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 ) );
}
