# ISS (Statistical Services) Statistics Paper III: Questions 16 - 21 of 109

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## Question number: 16

» 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

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## Question number: 17

» 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 the

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## Question number: 18

» 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

F

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## Question number: 19

» Econometrics » Pure and Mixed Estimation

Appeared in Year: 2009

### Write in Short

Discuss the problems involved in the statistical estimation of market demand function.

## Question number: 20

» Sampling Techniques » Concepts in Sampling

Appeared in Year: 2009

### Describe in Detail

What do you mean by sampling frame? Why do you need it? Give reasons for preferring the sampling to complete enumeration.

### Explanation

Sampling frame is a list of all the elements or things in the population from which the sample is drawn.

It is a list of all those within population which can be sampled, and may include individuals, households or institutions. To cover the population there should be some list, map or acceptable material called frame, which serves as a guide to cove

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## Question number: 21

» 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?