Other Estimation Methods

Abstract

Suppose that we have sample data x ₁, x ₂, …, x _n assumed to be observed values of independent random variables each having the same distribution function F where

$$\displaystyle{F(x) = \mathbb{P}(X \leq x)}$$

Define new random variables Z _i as the indicator functions of the interval (−∞, x], i.e.,

$$\displaystyle{Z_{i}(x) = \left \{\begin{array}{rl} 1&X_{i} \leq x\\ 0 &\mbox{ otherwise} \end{array} \right.}$$