function logpdf( x, alpha, beta ) {
	var out;
	if (
		isnan( x ) ||
		isnan( alpha ) ||
		isnan( beta ) ||
		alpha <= 0.0 ||
		beta <= 0.0
	) {
		return NaN;
	}
	if ( x < 0.0 || x > 1.0 ) {
		// Support of the Beta distribution: [0,1]
		return NINF;
	}
	if ( x === 0.0 ) {
		if ( alpha < 1.0 ) {
			return PINF;
		}
		if ( alpha > 1.0 ) {
			return NINF;
		}
		return ln( beta );
	}
	if ( x === 1.0 ) {
		if ( beta < 1.0 ) {
			return PINF;
		}
		if ( beta > 1.0 ) {
			return NINF;
		}
		return ln( alpha );
	}
	out = ( alpha-1.0 ) * ln( x );
	out += ( beta-1.0 ) * log1p( -x );
	out -= betaln( alpha, beta );
	return out;
}
Evaluates the natural logarithm of the probability density function (logPDF) 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 logPDF

@example
var y = logpdf( 0.5, 1.0, 1.0 );
// returns 0.0

@example
var y = logpdf( 0.5, 2.0, 4.0 );
// returns ~0.223

@example
var y = logpdf( 0.2, 2.0, 2.0 );
// returns ~-0.041

@example
var y = logpdf( 0.8, 4.0, 4.0 );
// returns ~-0.556

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

@example
var y = logpdf( 1.5, 4.0, 2.0 );
// returns -Infinity

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

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

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

@example
var y = logpdf( 0.5, NaN, 1.0 );
// returns NaN

@example
var y = logpdf( 0.5, 1.0, NaN );
// returns NaN