Cumulative distribution function
|
In probability theory, a cumulative distribution function F(x) of a probability density function say f(x) is a real valued and continuous function whose value is the proportion of probability values of a variable which occur on the part of the real line up and including the value of that variable; i.e.,
Considering this definition in light of the Fundamental Theorem of Calculus yields:
Due to the properties of the probability density function f(x), the cumulative distribution function F(x) will have the following properties:
(1) 
inside its domain of support.
(2) 
, i.e., finitely convergent (to unity by convention).
(3) 
for a<b, i.e., is non-decreasing
If the domain of the variable is finite, then the upper limit in equation (2) above should be the upper bound of the variables domain of support.
