A function giving the number of times, or proportional number of times, a set of random variables takes on a value lying within a specified interval conventionally, an interval having no lower limit (i.e., having a lower limit of -∞ . ) Alternatively, the total frequency with which a value equal to or less than a specified value of a random variable has occurred. It is also called a distrib-ution function, density function, cumulative frequency function, cumulative probability function and probability function. It is abbreviated as c. D. F. The term distribution function is preferred by many statisticians who consider cumulative distribution function a pleonasm. Unfortunately, distribution function now has several meanings, making the term ambiguous at best and vague at worst. Probability function is also ambiguous. Cumulative distribution function, on the other hand, has only one meaning at present and is therefore to be preferred where clarity is desired. Density function is most often used as a synonym for frequency function and its occurrence with the meaning of cumulative distribution function must be regarded as an aberration.