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Tribhuvan university CSIT 2065 Syllabus Simulation and modeling Old Questions 2068

Simulation and modeling - Old Questions

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3.  What is the main objective of gap test? Explain gap test algorithm with example.

10 marks
Asked in 2068

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The gap test is used to determine the significance of the interval between recurrence of the same digit. A gap of length x occurs between the recurrence of  some digit. It Counts the number of digits that appear between repetitions of a particular digit and then uses the Kolmogorov-Smirnov test to compare with the expected number of gaps. 

The probability of a particular gap length can be determined by a Bernoulli trail.

\\begin{displaymath}P ({\\rm gap ~of} ~ n) = P(x \\ne 3) P(x \\ne 3) ... P(x \\ne 3) P (x = 3) \\end{displaymath}

If we are only concerned with digits between 0 and 9, then

\\begin{displaymath}P ({\\rm gap ~of} ~ n) = 0.9^{n} 0.1 \\end{displaymath}

The theoretical frequency distribution for randomly ordered digits is given by

\\begin{displaymath}P (gap \\le x) = F(x) = 0.1 \\sum_{n=0}^x (0.9)^n = 1 - 0.9^{x+1} \\end{displaymath}

Steps involved in this test are:
Step 1:
   Specify the cdf for the theoretical frequency distribution given by Equation above based on the selected class interval width.
Step 2:
   Arrange the observed sample of gaps in a cumulative distribution with these same classes.
Step 3.
   Find D, the maximum deviation between F(x) and SN(x) as in equation D = max |F(x)-SN(x)|
Step 4.
   Determine the critical value, Dα, from Table( K-S critical value) for the specified value of  α and the sample size N.
Step 5.
   If the calculated value of D is greater than the tabulated value of Dα, the null hypothesis of independence is rejected.