Fuzzy Cumulative Distribution Function and its Properties

The statistical methods based on cumulative distribution function is a start point for many parametric or nonparametric statistical inferences . However , there are many practical problems that require dealing with observations that represent inherently imprecise. Applying a well-known definition of fuzzy random variables , this paper aims to extend the classical properties of a fuzzy cumulative distribution function induced by a family of continuous distribution functions with fuzzy parameters . The presented theoretical results will be illustrated with some lemmas and numerical examples .

کلیدواژه ها:

Cumulative distribution function ، fuzzy random variable ، ranking method ، convergence theorem ، divergence to infinity