# Logarithm of Probability Density Function

Weibull distribution logarithm of probability density function (PDF).

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

where lambda > 0 and k > 0 are the respective scale and shape parameters of the distribution.

## Usage

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


#### logpdf( x, k, lambda )

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

var y = logpdf( 2.0, 1.0, 0.5 );
// returns ~-3.297

y = logpdf( -1.0, 4.0, 2.0 );
// returns -Infinity


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

var y = logpdf( NaN, 1.0, 1.0 );
// returns NaN

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

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


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

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

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


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

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

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


#### logpdf.factory( k, lambda )

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

var mylogpdf = logpdf.factory( 2.0, 10.0 );

var y = mylogpdf( 12.0 );
// returns ~-2.865

y = mylogpdf( 5.0 );
// returns ~-2.551


## Examples

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

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