ISS (Statistical Services) Statistics Paper III: Questions 74 - 79 of 109

Let us consider the first order auto regressive model

… (i)

this is a linear difference equation of order 1. its complementary function (C. F.) is the so; ution of

which is a homogeneous linear difference equation of order 1.

if is the trial solution, then

ignoring the trivial solution

Hence complementary function (C. F) is

From (i) , E is the differ…

Sample mean is an unbiased estimator of population mean i.e..

Sample mean is given by

It can also be written as

Where

‎

Hence ‎

Variance of the estimator of the population total Y: :

Let us denote the Population Total Y as

The estimate of population total Y can be obtained by multiplying the estimate of mean by population size N.

Estimator of populatio…

link relative is the value of one season expressed as a percentage of the preceding season. The word ‘season’ refers to time period, it means month for monthly data, quarter for quarterly data etc.

Under this method, the seasonal indices are found with the following steps.

Steps:

(i) Find the link relative of all the seasonal data using the formulae

W…

Procedures for selecting a sample using probability proportional to size (PPS) scheme are:

• PPS sampling with Replacement
• PPS sampling without Replacement
• Cumulative total method
• Lahiri՚s method

An unbiased estimator of the population mean under PPS:

Let = value of the ith unit of the population , i = 1,2, … , N

= known value of the auxiliary variable fo…