function pdf( x, alpha, beta ) {
	var lnl;
	if (
		isnan( x ) ||
		isnan( alpha ) ||
		isnan( beta ) ||
		alpha <= 0.0 ||
		beta <= 0.0
	) {
		return NaN;
	}
	if ( x <= 0.0 ) {
		return 0.0;
	}
	lnl = (alpha * ln( beta )) - gammaln( alpha );
	lnl -= (alpha + 1.0) * ln( x );
	lnl -= beta / x;
	return exp( lnl );
}
Evaluates 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 PDF

@example
var y = pdf( 2.0, 0.5, 1.0 );
// returns ~0.121

@example
var y = pdf( 0.2, 1.0, 1.0 );
// returns ~0.168

@example
var y = pdf( -1.0, 4.0, 2.0 );
// returns 0.0

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

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

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

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

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