Cumulative Distribution Function

Weibull distribution cumulative distribution function.

The cumulative distribution function for a Weibull random variable is

upper F left-parenthesis x semicolon lamda comma k right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 1 minus e Superscript minus left-parenthesis x slash lamda right-parenthesis Super Superscript k Baseline 2nd Column x greater-than-or-equal-to 0 2nd Row 1st Column 0 2nd Column x less-than 0 EndLayout

where lambda > 0 is the shape parameter and k > 0 is the scale parameter.

Usage

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

cdf( x, k, lambda )

Evaluates the cumulative distribution function (CDF) for a Weibull distribution with shape parameter k and scale parameter lambda.

var y = cdf( 2.0, 1.0, 0.5 );
// returns ~0.982

y = cdf( 0.0, 1.0, 0.5 );
// 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.

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 k <= 0, the function returns NaN.

var y = cdf( 2.0, 0.5, -1.0 );
// returns NaN

y = cdf( 2.0, 0.5, 0.0 );
// returns NaN

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

var y = cdf( 2.0, 0.5, -1.0 );
// returns NaN

y = cdf( 2.0, 0.5, 0.0 );
// returns NaN

cdf.factory( k, lambda )

Returns a function for evaluating the cumulative distribution function of a Weibull distribution with shape parameter k and scale parameter lambda.

var mycdf = cdf.factory( 2.0, 10.0 );

var y = mycdf( 10.0 );
// returns ~0.632

y = mycdf( 8.0 );
// returns ~0.473

Examples

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

var lambda;
var k;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    lambda = randu() * 10.0;
    k = randu() * 10.0;
    y = cdf( x, lambda, k );
    console.log( 'x: %d, k: %d, λ: %d, F(x;k,λ): %d', x, k, lambda, y );
}