The statistical function that shows how the density of possible observations in a population is distributed. It is the derivative f(x) of the distribution function F(x) of a random variable, if F(x) is differentiable. Geometrically, f(x) is the ordinate of a curve such that f(x)dx yields the probability that the random variable will assume some value within the range dx of x. The density function is nonnegative, and its total integral is unity. Sometimes the probability density function is called the distribution function, but this practice causes confusion and is not recommended.