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# Additional Problems - TIA 4/C Seminar C.4 problems 1 Claim...

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TIA 4/C Seminar – C.4 problems 1. Claim sizes are modeled using an inverse Pareto distribution with τ = 2 and θ = 100. A random sample of losses is 350 450 600 900 Assuming that claims below 100 are truncated due to a deductible, calculate D(600). A. - 0 . 13 B. - 0 . 05 C. 0 . 05 D. 0 . 10 E. 0 . 12 2. Claim sizes are modeled using an inverse Pareto distribution with τ = 2 and θ = 100. A random sample of losses is 350 450 600 900 Assuming that claims below 100 are truncated due to a deductible, find the y -value of the point of a p - p plot that corresponds to the loss of 600. 3. Claim sizes are modeled using an inverse Pareto distribution with τ = 2 and θ = 100. A random sample of losses is 350 450 600 900 Assuming that claims below 100 are truncated due to a deductible, find the x -coordinate of the point of a p - p plot that corresponds to the loss of 600. 4. To compare a fitted model against the data, a D ( x ) plot is created. The D ( x ) plot contains the following values: x D ( x ) 0 0 100 -0.1 200 0.2 300 0.1 In which of the following intervals does the fitted model place greater weight than the observed data? c 2010 The Infinite Actuary, LLC p. 1 4/C Section C.4 Problems

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5. [C.F05.31] You are given: (i) The following are observed claim amounts: 400 1000 1600 3000 5000 5400 6200 (ii) An exponential distribution with θ = 3300 is hypothesized for the data. (iii) The goodness of fit is to be assessed by a p-p plot and a D ( x ) plot. Let ( s, t ) be the coordinates of the p-p plot for a claim amount of 3000. Determine ( s - t ) - D (3000). A. - 0 . 12 B. - 0 . 07 C. 0 . 00 D. 0 . 07 E. 0 . 12 6. [4.F04.38] You are given a random sample of observations: 0 . 1 0 . 2 0 . 5 0 . 7 1 . 3 You test the hypothesis that the probability density function is: f ( x ) = 4 (1 + x ) 5 , x > 0 Calculate the Kolmogorov-Smirnov test statistic. 7. [4.F02.17] You are given: (i) A sample of claim payments is: 29 64 90 135 182 (ii) Claim sizes are assumed to follow an exponential distribution. (iii) The mean of the exponential distribution is estimated using the method of moments. Calculate the value of the Kolmogorov-Smirnov test statistic. c 2010 The Infinite Actuary, LLC p. 2 4/C Section C.4 Problems
8. [C.S05.1] You are given: (i) A random sample of five observations from a population is: 0 . 2 0 . 7 0 . 9 1 . 1 1 . 3 (ii) You use the Kolmogorov-Smirnov test for testing the null hypothesis, H 0 , that the probability density function for the population is: f ( x ) = 4 (1 + x ) 5 , x > 0 (iii) Critical values for the Kolmogorov-Smirnov test are: Level of Significance 0.10 0.05 0.025 0.01 Critical Value 1 . 22 n 1 . 36 n 1 . 48 n 1 . 63 n Determine the result of the test.

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Additional Problems - TIA 4/C Seminar C.4 problems 1 Claim...

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