Mean

Weibull distribution expected value.

The expected value for a Weibull random variable is

double-struck upper E left-bracket upper X right-bracket equals lamda normal upper Gamma left-parenthesis 1 plus 1 slash k right-parenthesis

where k > 0 is the shape parameter λ > 0 is the scale parameter.

Usage

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

mean( k, lambda )

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

var v = mean( 1.0, 1.0 );
// returns 1.0

v = mean( 4.0, 12.0 );
// returns ~10.877

v = mean( 8.0, 2.0 );
// returns ~1.883

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

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

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

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

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

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

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

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

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

Examples

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

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 = mean( k, lambda );
    console.log( 'k: %d, λ: %d, E(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), v.toFixed( 4 ) );
}