Cumulative Distribution Function

Lévy distribution cumulative distribution function.

The cumulative distribution function for a Lévy random variable is

where mu is the location parameter and b > 0 is the scale parameter.

Usage

var cdf = require( '@stdlib/stats/base/dists/levy/cdf' );

cdf( x, mu, c )

Evaluates the cumulative distribution function (CDF) for a Lévy distribution with parameters mu (location parameter) and c > 0 (scale parameter).

var y = cdf( 2.0, 0.0, 1.0 );
// returns ~0.48

y = cdf( 12.0, 10.0, 3.0 );
// returns ~0.221

y = cdf( 9.0, 10.0, 3.0 );
// returns 0.0

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

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 NaN

If provided c <= 0, the function returns NaN.

var y = cdf( 2.0, 0.0, -1.0 );
// returns NaN

y = cdf( 2.0, 0.0, 0.0 );
// returns NaN

cdf.factory( mu, c )

Returns a function for evaluating the cumulative distribution function of a Lévy distribution with parameters mu (location parameter) and c > 0 (scale parameter).

var mycdf = cdf.factory( 3.0, 1.5 );

var y = mycdf( 4.0 );
// returns ~0.22

y = mycdf( 2.0 );
// returns 0.0

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var cdf = require( '@stdlib/stats/base/dists/levy/cdf' );

var mu;
var c;
var x;
var y;
var i;

for ( i = 0; i < 100; i++ ) {
    mu = randu() * 10.0;
    x = ( randu()*10.0 ) + mu;
    c = ( randu()*10.0 ) + EPS;
    y = cdf( x, mu, c );
    console.log( 'x: %d, µ: %d, c: %d, F(x;µ,c): %d', x.toFixed( 4 ), mu.toFixed( 4 ), c.toFixed( 4 ), y.toFixed( 4 ) );
}