Introduction to Estimation

From our pervious knowledge we are now able to distinguish between a population and a sample, parameter and statistic, random and non-random sampling. We also have a little knowledge of some sampling distributions. The difficulty in dealing with population is that we usually do not know the value of their parameters. Even if we could find these values, it is not desirable at the cost of time, money and reliability.

This area is being devoted to the study of most suitable values of these parameters based on the random samples, from the given population. These values, which are functions of sample observations, derived on the basis of a certain criterion, are called the “estimates”. The formulae with which these estimates are obtained are called “estimators”. The methods by which we extract information about the population on the basis of samples is called “estimation”.

The problem of estimation is the problem of determining most probable values of the parameters of probability distributions. For example, let the problem is to estimate the average height of the individuals in M.Sc class during 2000. A researcher then draws a sample of few individual and on the basis of the information obtained from the sample might express his view by saying that

  1. the average height of the individuals is 65 inches, or
  2. most probably the average height is between 62 and 67 inches

We therefore, have two kinds of estimates. An estimate of the type given in (1) above, which is known as a “Point Estimate” and an estimate of the type given in (2) above, which is known as “Interval Estimate”.