Logarithm of Cumulative Distribution Function

Arcsine distribution logarithm of cumulative distribution function.

The cumulative distribution function for an arcsine random variable is

where a is the minimum support and b is the maximum support. The parameters must satisfy a < b.

Usage

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

logcdf( x, a, b )

Evaluates the logarithm of the cumulative distribution function (CDF) for an arcsine distribution with parameters a (minimum support) and b (maximum support).

var y = logcdf( 9.0, 0.0, 10.0 );
// returns ~-0.23

y = logcdf( 0.5, 0.0, 2.0 );
// returns ~-1.1

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

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

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

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

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

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

If provided a >= b, the function returns NaN.

var y = logcdf( 1.0, 2.5, 2.0 );
// returns NaN

logcdf.factory( a, b )

Returns a function for evaluating the logarithm of the cumulative distribution function of an arcsine distribution with parameters a (minimum support) and b (maximum support).

var mylogcdf = logcdf.factory( 0.0, 10.0 );
var y = mylogcdf( 0.5 );
// returns ~-1.941

y = mylogcdf( 8.0 );
// returns ~-0.35

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/arcsine/logcdf' );

var a;
var b;
var x;
var y;
var i;

for ( i = 0; i < 25; i++ ) {
    x = ( randu()*20.0 ) - 10.0;
    a = ( randu()*20.0 ) - 20.0;
    b = a + ( randu()*40.0 );
    y = logcdf( x, a, b );
    console.log( 'x: %d, a: %d, b: %d, ln(F(x;a,b)): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}