A probability density function (PDF) is a function of a continuous uncertain variable whose integral over any interval gives the probability that the variable's outcome will fall within that interval. When the uncertain variable is a random variable (ie, when its range is strictly numerical), two related functions are defined with respect to this integral: for semi-infinite intervals bounded on the top, the integral is referred to as the variable's cumulative distribution function; for semi-infinite intervals bounded on the bottom, the integral is referred to as the variable's excess distribution function.

See also: Background State of Information, Probability Distribution.