# Applied Statistics (ISS (Statistical Services) Statistics Paper III): Questions 6 - 12 of 45

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## Question number: 6

» Applied Statistics » Index Numbers » Link and Chain Relatives Composition of Index Numbers

Appeared in Year: 2009

### Write in Short

Explain the time reversal and factor-reversal tests for an ideal index number. Give an example

of index number which satisfies both of these tests.

## Question number: 7

» Applied Statistics » Index Numbers » Income Distribution-Pareto and Engel Curves

Appeared in Year: 2009

### Describe in Detail

State the probability density function of the Pareto distribution and give its cumulative form.

Interpret the constants involved.

### Explanation

**Probability Density Function of the Pareto distribution: **

Suppose that X has the Pareto distribution with shape parameter a∈ (0, ∞) and scale parameter b∈ (0, ∞) then X has probability density function f given by

where is the (necessarily positive) minimum possible value of X, and α is a positive parameter.

Pareto Type

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## Question number: 8

» Applied Statistics » Time Series Analysis » Determination of Trend, Seasonal and Cyclical Fluctuations

Appeared in Year: 2009

### Describe in Detail

Explain ratio to moving average method for calculating seasonal indices.

### Explanation

Ratio to moving average method is an improvement over the ‘ratio to trend’ method as it removes the cyclic fluctuations, which remain closely mixed with the seasonal indices calculated under ‘ratio to trend method’. Here seasonal indices are calculated based on the moving average trend instead of a least square trend.

Further, both the trend and

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## Question number: 9

» Applied Statistics » Index Numbers » Fisher Index Numbers: Chain Base Index Number & Tests for Index Number

Appeared in Year: 2009

### Describe in Detail

Define Marshall- Edgeworth index number and examine whether it satisfies Fisher’s tests for index numbers. Also show that this index number will lie between the Laspeyres’ and Paasche’s index numbers.

### Explanation

**Marshall- Edgeworth Index Number: **

In this index number, the average of the quantities of the base year and current year are used as weights. Thus, the weight of an item would be . Accordingly the formula of index number is:

= X 100

OR

= X 100

Fisher’s tests for Marshall- Edgeworth Index Numb

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## Question number: 10

» Applied Statistics » Computations Based on Fourier Transform

Appeared in Year: 2009

### Write in Short

Describe, briefly, the Engel’s law and Engel’s curve. What are the different forms of Engel’s

Curve usually employed for fitting to the family budget data?

## Question number: 11

» Applied Statistics » Spectral Analysis of Weakly Stationary Process

Appeared in Year: 2009

### Describe in Detail

Distinguish between fixed base and chain base methods for the construction of index numbers.

Discuss their relative merits.

### Explanation

**Fixed base method: ** In this method, the base year remains fixed for all the years of calculation. The base year price (quantity) selected may be the price of a given year or the average of prices of a given number of years. In the absence of any instruction to this effect, the foremost year’s price is taken as the base year’s price. Formula for ca

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## Question number: 12

» Applied Statistics » Time Series Analysis » Economic Time Series & Components

Appeared in Year: 2009

### Write in Short

Describe the Yule -Slutsky effect of moving average operation on the random component of a time series.