Cumulative Distribution Function

Degenerate distribution cumulative distribution function.

The cumulative distribution function for a degenerate random variable is

upper F left-parenthesis x semicolon mu right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 1 comma 2nd Column x greater-than-or-equal-to mu comma 2nd Row 1st Column 0 comma 2nd Column x less-than mu period EndLayout

where µ is the constant value of the distribution.

Usage

var cdf = require( '@stdlib/math/base/dists/degenerate/cdf' );

cdf( x, mu )

Evaluates the CDF of a degenerate distribution centered at mu.

var y = cdf( 2.0, 8.0 );
// returns 0.0

y = cdf( 8.0, 8.0 );
// returns 1.0

y = cdf( 10.0, 8.0 );
// returns 1.0

cdf.factory( mu )

Returns a function for evaluating the cumulative distribution function of a degenerate distribution centered at mu.

var mycdf = cdf.factory( 10.0 );

var y = mycdf( 10.0 );
// returns 1.0

y = mycdf( 8.0 );
// returns 0.0

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var cdf = require( '@stdlib/math/base/dists/degenerate/cdf' );

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

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