1. The number of claims in a month for a portfolio of insurance policies is thought...

1. The number of claims in a month for a portfolio of insurance policies is thought to follow the Negative-binomial distribution with pdf

?(?) =( Γ(20+?) / Γ(? +1)Γ(20) ) . ?^20 . (1−?)^?, ? = 0,1,2,…

A sample of 4 months had claim numbers of 15, 25, 20 and 21.

a) There is no prior information for p. Using an uninformative prior to derive the posterior distribution for p. [12 marks]

b) Show that the mode of the Beta distribution with pdf ?(?) =( Γ(? +?) / Γ(?)Γ(?) ) . ?^(?−1) . (1−?)^(?−1), 0 < ? < 1

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Consider a portfolio of insurance policies, on which the number of claims has a binomial distribution...

Consider a portfolio of insurance policies, on which the number of claims has a binomial distribution with parameters n = 1,000 and p = 0.01. The claim size distribution is assumed to be exponential with mean $100. Claim amounts are assumed to be independent random variables, and the claim amounts are independent of the number of claims. The insurer takes out an individual excess of loss reinsurance contract with a retention level of $200. Calculate the mean of the aggregate...

An insurance company issues 1600 vision care insurance policies. The number of claims filed by a...

An insurance company issues 1600 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a Poisson random variable with mean 5. Assume the numbers of claims filed by distinct policyholders are independent of one another. Find the approximate probability that the number of total claims during a one-year period is between 7928 and 8197.

The number of successful claims on life insurance policies for an insurance company has been determined...

The number of successful claims on life insurance policies for an insurance company has been determined to follow a Poisson process with an average rate of 5 claims per week. If the amount of money paid on each policy is uniformly distributed between $2,000 and $10,000, what is the mean of the total amount of money that the company pays out in a four-week period?

An insurance company issues 1250 vision care insurance policies. The number of claims filed by a...

An insurance company issues 1250 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a Poisson random variable with mean 2. Assume the numbers of claims filed by a distinct policyholders are independent of one another. What is the approximate probability that there is a total of between 2450 and 2600 claims during a one year period?

Imagine that an insurance company claims 7 policies on average per month. Calculate the probability that...

Imagine that an insurance company claims 7 policies on average per month. Calculate the probability that no policy will be claimed in a week

1. A insurance office keeps track of the number of car insurance claims filed each day....

1. A insurance office keeps track of the number of car insurance claims filed each day. Based on the data collected, it determines that the following probability distribution applies: Number of Claims Probability 0 .05 1 .15 2 .25 3 .45 4 .10 a. What is the expected number of new claims filed each day? b. If a claim pays out on average $5000, what is the average cost per day? c. If the ofice is open 250 days a...

7 - The annual claims made by clients on their insurance policies have an average of...

7 - The annual claims made by clients on their insurance policies have an average of 8 million dollars and a standard deviation of 1.5 million dollars. If the amounts can be assumed to have a normal distribution, find the probability that the annual claims in 1 year is (a) Greater than 10 million dollars, (b) Between 6 million and 9 million dollars, (c) Either less than 7 million or greater than 10 million dollars and, (d) Find the annual...

Claims arrive to an insurance company according to a Poisson Process. The average number of claims...

Claims arrive to an insurance company according to a Poisson Process. The average number of claims reported every day is 2.5. It has been reported that 15% of these claims are fake. What is the probability that in a week of five business day 10 claims arrive and one of these is fake? ONLY ANSWERRRRR

1. An insurer has a portfolio of 1000 independent one-year term insurance policies. For any one...

1. An insurer has a portfolio of 1000 independent one-year term insurance policies. For any one policy, there is a probability of 0.01 that there will be a claim. Use the normal approximation to find the probability that the insurer will experience at least 10 claims using the integer correction.

. A researcher claims that the number of homicide crimes in California by month is uniformly...

. A researcher claims that the number of homicide crimes in California by month is uniformly distributed. To test this claim, you randomly select 1200 homicides from a recent year and record the month when each happened. The table below shows the results. At a 10% level of significance, test the researchers claim. Month Frequency January 115 February 75 March 90 April 98 May 121 June 99 July 115 August 98 September 92 October 108 November 90 December 99

Subjects