Logarithm of Cumulative Distribution Function

Evaluate the natural logarithm of the cumulative distribution function for a beta prime distribution .

The cumulative distribution function for a beta prime random variable is

where alpha > 0 is the first shape parameter, beta > 0 is the second shape parameter and I is the incomplete beta function.

Usage

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

logcdf( x, alpha, beta )

Evaluates the natural logarithm of the cumulative distribution function (CDF) for a beta prime distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var y = logcdf( 0.5, 1.0, 1.0 );
// returns ~-1.099

y = logcdf( 0.5, 2.0, 4.0 );
// returns ~-0.618

y = logcdf( 0.2, 2.0, 2.0 );
// returns ~-2.603

y = logcdf( 0.8, 4.0, 4.0 );
// returns ~-0.968

y = logcdf( -0.5, 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 alpha <= 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 beta <= 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( alpha, beta )

Returns a function for evaluating the natural logarithm of the cumulative distribution function for a beta prime distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var mylogcdf = logcdf.factory( 0.5, 0.5 );

var y = mylogcdf( 0.8 );
// returns ~-0.767

y = mylogcdf( 0.3 );
// returns ~-1.143

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 EPS = require( '@stdlib/constants/float64/eps' );
var logcdf = require( '@stdlib/stats/base/dists/betaprime/logcdf' );

var alpha;
var beta;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu();
    alpha = ( randu()*5.0 ) + EPS;
    beta = ( randu()*5.0 ) + EPS;
    y = logcdf( x, alpha, beta );
    console.log( 'x: %d, α: %d, β: %d, ln(F(x;α,β)): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}