function logcdf( x, alpha, beta ) {
	if (
		isnan( x ) ||
		isnan( alpha ) ||
		isnan( beta ) ||
		alpha <= 0.0 ||
		beta <= 0.0
	) {
		return NaN;
	}
	if ( x <= 0.0 ) {
		return NINF;
	}
	if ( x >= 1.0 ) {
		return 0.0;
	}
	return ln( betainc( x, alpha, beta ) );
}
Evaluates the natural logarithm of the cumulative distribution function (CDF) for a beta distribution with first shape parameter `alpha` and second shape parameter `beta` at a value `x`.

@param {number} x - input value
@param {PositiveNumber} alpha - first shape parameter
@param {PositiveNumber} beta - second shape parameter
@returns {number} evaluated logCDF

@example
var y = logcdf( 0.5, 1.0, 1.0 );
// returns ~-0.693

@example
var y = logcdf( 0.5, 2.0, 4.0 );
// returns ~-0.208

@example
var y = logcdf( 0.2, 2.0, 2.0 );
// returns ~-2.263

@example
var y = logcdf( 0.8, 4.0, 4.0 );
// returns ~-0.034

@example
var y = logcdf( -0.5, 4.0, 2.0 );
// returns -Infinity

@example
var y = logcdf( 1.5, 4.0, 2.0 );
// returns 0.0

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

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

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

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

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