Cumulative Distribution Function

Studentized range distribution cumulative distribution function (CDF).

Usage

var cdf = require( '@stdlib/stats/base/dists/studentized-range/cdf' );

cdf( x, r, v[, nranges=1] )

Evaluates the cumulative distribution function (CDF) for a studentized range distribution with sample size r and v degrees of freedom. Optionally, the number of groups whose maximum range is considered can be specified via the nranges parameter.

var y = cdf( 0.5, 3.0, 2.0 );
// returns ~0.0644

y = cdf( 12.1, 17.0, 2.0 );
// returns ~0.913

y = cdf( 0.5, 3.0, 2.0, 2 );
// returns ~0.01

If provided NaN as any argument, the function returns NaN.

var y = cdf( NaN, 2.0, 2.0 );
// returns NaN

y = cdf( 1.5, NaN, 2.0 );
// returns NaN

If provided v < 2 or r < 2, the function returns NaN.

var y = cdf( 2.0, -1.0, 3.0 );
// returns NaN

y = cdf( 2.0, 3.0, 1.5 );
// returns NaN

cdf.factory( r, v[, nranges=1] )

Returns a function for evaluating the cdf of a studentized range distribution with sample size r and v degrees of freedom. Optionally. Optionally, the number of groups whose maximum range is considered can be specified via the nranges parameter.

var mycdf = cdf.factory( 3.0, 2.0 );
var y = mycdf( 3.0 );
// returns ~0.712

y = mycdf( 1.0 );
// returns ~0.216

Examples

var randu = require( '@stdlib/random/base/randu' );
var cdf = require( '@stdlib/stats/base/dists/studentized-range/cdf' );

var v;
var q;
var r;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    q = randu() * 12.0;
    r = ( randu() * 20.0 ) + 2.0;
    v = ( randu() * 10.0 ) + 2.0;
    y = cdf( q, r, v );
    console.log( 'q: %d, r: %d, v: %d, F(x;v): %d', q.toFixed( 4 ), r.toFixed( 4 ), v.toFixed( 4 ), y.toFixed( 4 ) );
}