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POINT ESTIMATOR OF
PARAMETERS
Definition 15.2.
Let X ~𝑓 𝑥, 𝜃 𝑎𝑛𝑑 𝑥1, 𝑥2, 𝑥3, 𝑥4, …. 𝑥𝑛, be a random sample
from the population X. Any statistic that can be used to guess the parameter
𝜃 is called an estimator of 𝜃. The numerical value of this statistic is called
an estimate of 𝜃. The estimator of the parameter 𝜃 is denoted by𝜃.
One of the basic problems is how to find an estimator of population
parameter 𝜃. There are several methods for finding an estimator of 𝜃. Some
of these methods are:
(1) Maximum Likelihood Method
(2) Moment Method
(3) Bayes Method
(4) Least Squares Method
(5) Minimum Chi-Squares Method
(6) Minimum Distance Method
15.1. Moment Method
Example 15.4.
Let X1,X2, ...,Xn be a random sample of size n from a population X with probability density
function
15.2. Maximum Likelihood Method
Example 15.9.
If X1,X2, ...,Xn is a random sample from a distribution with density function