# Distribution function

From Glossary of Meteorology

## 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.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.