Logarithm of Cumulative Distribution Function

Arcsine distribution logarithm of cumulative distribution function.

The cumulative distribution function for an arcsine random variable is

upper F left-parenthesis x right-parenthesis equals StartFraction 2 Over pi EndFraction arc sine left-parenthesis StartRoot StartFraction x minus a Over b minus a EndFraction EndRoot right-parenthesis

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

Usage

var logcdf = require( '@stdlib/math/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 = cdf.factory( 0.0, 10.0 );
var y = mylogcdf( 0.5 );
// returns ~-1.938

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

Examples

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