This article is simply wrong That probability integral looks all kinds of fancy and all but having spent my life in finance I have never yet known anybody who claimed to know the pdf of the returns I suppose that if I knew such a pdf I would not be very interested in calculating statistics The Sortino ratio is a statistic and everything except the target return that goes into it is a statistic That DR in this vapid article is a functional of some unknown pdf which is completely useless for anything practical You could fix this up by making that some empirical pdf but that is pedantic and stupid