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 ) {
		return NINF;
	}
	out = (alpha * ln( beta )) - gammaln( alpha );
	out -= (alpha + 1.0) * ln( x );
	out -= beta / x;
	return out;
}
Evaluates the natural logarithm of the probability density function (PDF) for an inverse gamma distribution with shape parameter `alpha` and scale parameter `beta` at a value `x`.

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

@example
var y = logpdf( 2.0, 0.5, 1.0 );
// returns ~-2.112

@example
var y = logpdf( 0.2, 1.0, 1.0 );
// returns ~-1.781

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

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