1. POINT ESTIMATOR OF PARAMETERS
Definition 15.2.
Let X ~𝑓 𝑥,𝜃 𝑎𝑛𝑑 𝑥 1, 𝑥 2, 𝑥 3, 𝑥 4, …. 𝑥 𝑛, 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 by 𝜃 .
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:
Maximum Likelihood Method
(2) Moment Method
(3) Bayes Method
(4) Least Squares Method
(5) Minimum Chi-Squares Method
(6) Minimum Distance Method

2. 15.1. Moment Method

6. Example 15.4.
Let X1,X2, ...,Xn be a random sample of size n from a population X with probability density function

9. 15.2. Maximum Likelihood Method

10. Example 15.9.
If X1,X2, ...,Xn is a random sample from a distribution with density function