Logarithm of Cumulative Distribution Function

Weibull distribution logarithm of cumulative distribution function.

The cumulative distribution function for a Weibull random variable is

Cumulative distribution function for a Weibull distribution.

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

Usage

var logcdf = require( '@stdlib/math/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

Examples

var randu = require( '@stdlib/random/base/randu' );
var logcdf = require( '@stdlib/math/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 );
}