# Distribution function

From AMS Glossary

## distribution function

(

*Also called*probability distribution function.) 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*(*x*_{2}) ≥*F*(*x*_{1}) whenever*x*_{2}>*x*_{1}. Sometimes, for the sake of clarity, the distribution function is called the cumulative distribution function.*Compare*probability density function.