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

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