function pdf( 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 0.0;
	}
	if ( x === 0.0 ) {
		if ( alpha < 1.0 ) {
			return PINF;
		}
		if ( alpha > 1.0 ) {
			return 0.0;
		}
		return beta;
	}
	if ( x === 1.0 ) {
		if ( beta < 1.0 ) {
			return PINF;
		}
		if ( beta > 1.0 ) {
			return 0.0;
		}
		return alpha;
	}
	out = ( alpha-1.0 ) * ln( x );
	out += ( beta-1.0 ) * log1p( -x );
	out -= betaln( alpha, beta );
	return exp( out );
}
Evaluates the probability density function (PDF) 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 PDF

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

@example
var y = pdf( 0.5, 2.0, 4.0 );
// returns 1.25

@example
var y = pdf( 0.2, 2.0, 2.0 );
// returns ~0.96

@example
var y = pdf( 0.8, 4.0, 4.0 );
// returns ~0.573

@example
var y = pdf( -0.5, 4.0, 2.0 );
// returns 0.0

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

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

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

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

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

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