Median

Weibull distribution median.

The median for a Weibull random variable is

upper M e d i a n left-parenthesis upper X right-parenthesis equals lamda left-parenthesis ln left-parenthesis 2 right-parenthesis right-parenthesis Superscript 1 slash k

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

Usage

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

median( k, lambda )

Returns the median of a Weibull distribution with parameters k (shape parameter) and lambda (scale parameter).

var v = median( 1.0, 1.0 );
// returns ~0.693

v = median( 4.0, 12.0 );
// returns ~10.949

v = median( 8.0, 2.0 );
// returns ~1.91

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

var v = median( NaN, 2.0 );
// returns NaN

v = median( 2.0, NaN );
// returns NaN

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

var v = median( 0.0, 1.0 );
// returns NaN

v = median( -1.0, 1.0 );
// returns NaN

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

var v = median( 1.0, 0.0 );
// returns NaN

v = median( 1.0, -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/math/float64-eps' );
var median = require( '@stdlib/math/base/dists/weibull/median' );

var lambda;
var k;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    k = ( randu()*10.0 ) + EPS;
    lambda = ( randu()*10.0 ) + EPS;
    v = median( k, lambda );
    console.log( 'k: %d, λ: %d, Median(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), v.toFixed( 4 ) );
}