Mode

Weibull distribution mode.

The mode for a Weibull random variable is

m o d e left-parenthesis upper X right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column lamda left-parenthesis StartFraction k minus 1 Over k EndFraction right-parenthesis Superscript StartFraction 1 Over k EndFraction Baseline 2nd Column k greater-than 1 2nd Row 1st Column 0 2nd Column k less-than-or-equal-to 1 EndLayout

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

Usage

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

mode( k, lambda )

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

var v = mode( 4.0, 12.0 );
// returns ~11.167

v = mode( 8.0, 2.0 );
// returns ~1.967

If provided 0 < k <= 1, the function returns 0.0.

var v = mode( 1.0, 1.0 );
// returns 0.0

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

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

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

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

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

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

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

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

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

Examples

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

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