Probability Density Function

Weibull distribution probability density function (PDF).

The probability density function (PDF) for a Weibull random variable is

f left-parenthesis x semicolon lamda comma k right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column StartFraction k Over lamda EndFraction left-parenthesis StartFraction x Over lamda EndFraction right-parenthesis Superscript k minus 1 Baseline 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 and k > 0 are the respective scale and shape parameters of the distribution.

Usage

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

pdf( x, k, lambda )

Evaluates the probability density function (PDF) for a Weibull distribution with shape parameter k and scale parameter lambda.

var y = pdf( 2.0, 1.0, 0.5 );
// returns ~0.037

y = pdf( -1.0, 4.0, 2.0 );
// returns 0.0

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

var y = pdf( NaN, 0.0, 1.0 );
// returns NaN

y = pdf( 0.0, NaN, 1.0 );
// returns NaN

y = pdf( 0.0, 0.0, NaN );
// returns NaN

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

var y = pdf( 2.0, 0.0, 1.0 );
// returns NaN

pdf( 2.0, -1.0, 1.0 );
// returns NaN

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

var y = pdf( 2.0, 1.0, 0.0 );
// returns NaN

y = pdf( 2.0, 1.0, -1.0 );
// returns NaN

pdf.factory( k, lambda )

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

var mypdf = pdf.factory( 2.0, 10.0 );

var y = mypdf( 12.0 );
// returns ~0.057

y = mypdf( 5.0 );
// returns ~0.078

Examples

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

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 = pdf( x, lambda, k );
    console.log( 'x: %d, k: %d, λ: %d, f(x;k,λ): %d', x.toFixed( 4 ), k.toFixed( 4 ), lambda.toFixed( 4 ), y.toFixed( 4 ) );
}