Question

What does i.i.d. stand for in econometrics?

Answer 1

Answer:-

i.i.d. stands for independent and identically distributed .

In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent.This property is usually abbreviated as i.i.d. or iid or IID. Herein, i.i.d. is used, because it is the most prevalent.

• Identically Distributed means that there are no overall trends–the distribution doesn’t fluctuate and all items in the sample are taken from the same probability distribution.
• Independent means that the sample items are all independent events. In other words, they aren’t connected to each other in any way.

                                                           Explanation:-

=> Suppose that the random variables   and are defined to assume values in . Let

and be the cumulative distribution functions of and ,

respectively, and denote their joint cumulative distribution function by

.

=> Two random variables and are identically distributed if and only if .

=> Two random variables and are independent if and only if

.

=> Two random variables and are i.i.d. if they are independent and identically distributed, i.e. if and only if