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/stats/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 ~-3.307

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 ~-2.867

y = mylogpdf( 5.0 );
// returns ~-2.553

Notes

In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.

Examples

var randu = require( '@stdlib/random/base/randu' );
var logpdf = require( '@stdlib/stats/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 ) );
}