A function F(x) yielding the probability that a stated random variable will assume some value less than or equal to any arbitrary number x. By definition, the distribution function is identically zero for all values of x below the least admissible value of the random variable, and identically unity for all values of x equal to or greater than the greatest admissible value of the random variable. Moreover, F(x2) ≥ F(x1) whenever x2 > x1. Sometimes, for the sake of clarity, the distribution function is called the cumulative distribution function. Compare probability density function.