function logpdf( x, alpha, beta ) {
	if (
		isnan( x ) ||
		isnan( alpha ) ||
		isnan( beta ) ||
		alpha < 0.0 ||
		beta <= 0.0
	) {
		return NaN;
	}
	if ( x < 0.0 || x === PINF ) {
		return NINF;
	}
	if ( alpha === 0.0 ) {
		// Point mass at 0...
		return ( x === 0.0 ) ? PINF : NINF;
	}
	return ln( gammaDeriv( alpha, x * beta ) ) + ln( beta );
}
Evaluates the logarithm of the probability density function (PDF) for a gamma distribution with shape parameter `alpha` and rate parameter `beta` at a value `x`.

@param {number} x - input value
@param {NonNegativeNumber} alpha - shape parameter
@param {PositiveNumber} beta - rate parameter
@returns {number} evaluated logPDF

@example
var y = logpdf( 2.0, 0.5, 1.0 );
// returns ~-2.919

@example
var y = logpdf( 0.1, 1.0, 1.0 );
// returns ~-0.1

@example
var y = logpdf( -1.0, 4.0, 2.0 );
// returns -Infinity

@example
var y = logpdf( NaN, 0.6, 1.0 );
// returns NaN

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

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

@example
// Negative shape parameter:
var y = logpdf( 2.0, -1.0, 1.0 );
// returns NaN

@example
// Negative rate parameter:
var y = logpdf( 2.0, 1.0, -1.0 );
// returns NaN