Logarithm of Cumulative Distribution Function

Weibull distribution logarithm of cumulative distribution function.

The cumulative distribution function for a Weibull random variable is

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

Usage

var logcdf = require( '@stdlib/stats/base/dists/weibull/logcdf' );

logcdf( x, k, lambda )

Evaluates the natural logarithm of the cumulative distribution function (CDF) for a Weibull distribution with shape parameter k and scale parameter lambda.

var y = logcdf( 2.0, 1.0, 0.5 );
// returns ~-0.018

y = logcdf( 0.0, 0.5, 1.0 );
// returns -Infinity

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

y = logcdf( +Infinity, 4.0, 2.0 );
// returns 0.0

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

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

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

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

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

var y = logcdf( 2.0, -1.0, 0.5 );
// returns NaN

y = logcdf( 2.0, 0.0, 0.5 );
// returns NaN

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

var y = logcdf( 2.0, 0.5, -1.0 );
// returns NaN

y = logcdf( 2.0, 0.5, 0.0 );
// returns NaN

logcdf.factory( k, lambda )

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

var mylogcdf = logcdf.factory( 2.0, 10.0 );

var y = mylogcdf( 10.0 );
// returns ~-0.459

y = mylogcdf( 8.0 );
// returns ~-0.749

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 logcdf = require( '@stdlib/stats/base/dists/weibull/logcdf' );

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 = logcdf( x, lambda, k );
    console.log( 'x: %d, k: %d, λ: %d, ln(F(x;k,λ)): %d', x, k, lambda, y );
}