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Marine losses for an oil company. The frequency
Chapter 4, Problem 146E(choose chapter or problem)
Problem 146E
Marine losses for an oil company. The frequency distribution shown in the next table depicts the property and marine losses incurred by a large oil company over the last 2 years. This distribution can be used by the company to predict future losses and to help determine an appropriate level of insurance coverage. In analyzing the losses within an interval of the distribution, for simplification, analysts may treat the interval as a uniform probability distribution (Research Review, Summer 1998). In the insurance business, intervals like these are often called layers.
Layer |
Property and MarineLosses (millions of $) |
Frequency |
1 |
0.00–0.01 |
668 |
2 |
0.01–0.05 |
38 |
3 |
0.05–0.10 |
7 |
4 |
0.10–0.25 |
4 |
5 |
0.25–0.50 |
2 |
6 |
0.50–1.00 |
1 |
7 |
1.00–2.50 |
0 |
Source: Based on Cozzolino, J. M., & Mikolaj, P. J. “Applications of the piecewise constant pareto distribution,” Research Review, Summer 1998, pp. 39–59.
a. Use a uniform distribution to model the loss amount in layer 2. Graph the distribution. Calculate and interpret its mean and variance.
b. Repeat part a for layer 6.
c. If a loss occurs in layer 2, what is the probability that it exceeds $10,000? That it is under $25,000?
d. If a layer-6 loss occurs, what is the probability that it is between $750,000 and $1,000,000? That it exceeds $900,000? That it is exactly $900,000?
Questions & Answers
QUESTION:
Problem 146E
Marine losses for an oil company. The frequency distribution shown in the next table depicts the property and marine losses incurred by a large oil company over the last 2 years. This distribution can be used by the company to predict future losses and to help determine an appropriate level of insurance coverage. In analyzing the losses within an interval of the distribution, for simplification, analysts may treat the interval as a uniform probability distribution (Research Review, Summer 1998). In the insurance business, intervals like these are often called layers.
Layer |
Property and MarineLosses (millions of $) |
Frequency |
1 |
0.00–0.01 |
668 |
2 |
0.01–0.05 |
38 |
3 |
0.05–0.10 |
7 |
4 |
0.10–0.25 |
4 |
5 |
0.25–0.50 |
2 |
6 |
0.50–1.00 |
1 |
7 |
1.00–2.50 |
0 |
Source: Based on Cozzolino, J. M., & Mikolaj, P. J. “Applications of the piecewise constant pareto distribution,” Research Review, Summer 1998, pp. 39–59.
a. Use a uniform distribution to model the loss amount in layer 2. Graph the distribution. Calculate and interpret its mean and variance.
b. Repeat part a for layer 6.
c. If a loss occurs in layer 2, what is the probability that it exceeds $10,000? That it is under $25,000?
d. If a layer-6 loss occurs, what is the probability that it is between $750,000 and $1,000,000? That it exceeds $900,000? That it is exactly $900,000?
ANSWER:
Step 1 of 8
a. Let x denotes model the loss amount in layer 2 and the random variable x has the uniform with c = 0.01 and d = 005 millions of dollars.
First we convert the dollars into million dollars into dollars; we multiply the losses into 1,000,000.
That is c = $10,000 and d = $50,000
The probability density function, f (x) of random variable x is given as follows:
