2. Loss Amount: 0-1000 # of Losses: 5
Loss Amount: 1000-5000 # of Losses: 4
Loss Amount: 5000-10000 # of Losses: 3
An ogive is used as a model for loss sizes. Determine the fitted median.
F(1000) = 5/12
F(5000) = 9/12
m-1000/5000-1000 = 0.5 - 5/12 / 9/12 - 5/12
My question is how is the above relationship possible?
11. An auto collision coverage is sold with deductibles of 500 and 1000. You have the following info for total loss size on 86 claims:
Deductible 1000:
Loss size: (1000-2000) # of losses: 20
Loss size: over 2000 # of losses: 10
Deductible 500:
Loss size: (500-1000) # of losses: 32
Loss size: Over 1000 # of losses: 24
Ground up underlying losses for both deductibles are assumed to follow an exponential distribution with the same parameter. You estimate the parameter using MLE. For policies with an ordinary deductible 500, determine the fitted average total loss size for losses on which non-zero claim payments are made.
L(theta) = (1-e^-1000/theta)^20 (e^-1000/theta)^10 (1-e^-500/theta)^32 (e^-500/theta) ^24
theta = 707.3875
answer: 707.3875 + 500 = 1207.3875
How did they get the L(theta)? why is the deductible used as x? why do you add 500 at the end?
17. You are given:
1) Annual claim counts follow a Poisson distribution with mean lambda.
2) Lambda varies by insured. The distribution over all insureds is normal with mean 0.6 and variance is 0.04.
3) An insured is selected at random and claim counts over 3 years are simulated for this insured by first simulating lambda and then simulating each year's claim counts.
4) All simulations are done using the inversion method.
Uniform numbers in order : .28, .32, .13, .94
Determine the total number of simulated claims over three years.
lambda = 0.6 + inverse phi (.28) * rad .04 = .484
how did know to do that with lambda?
Any help would be greatly appreciated.
Loss Amount: 1000-5000 # of Losses: 4
Loss Amount: 5000-10000 # of Losses: 3
An ogive is used as a model for loss sizes. Determine the fitted median.
F(1000) = 5/12
F(5000) = 9/12
m-1000/5000-1000 = 0.5 - 5/12 / 9/12 - 5/12
My question is how is the above relationship possible?
11. An auto collision coverage is sold with deductibles of 500 and 1000. You have the following info for total loss size on 86 claims:
Deductible 1000:
Loss size: (1000-2000) # of losses: 20
Loss size: over 2000 # of losses: 10
Deductible 500:
Loss size: (500-1000) # of losses: 32
Loss size: Over 1000 # of losses: 24
Ground up underlying losses for both deductibles are assumed to follow an exponential distribution with the same parameter. You estimate the parameter using MLE. For policies with an ordinary deductible 500, determine the fitted average total loss size for losses on which non-zero claim payments are made.
L(theta) = (1-e^-1000/theta)^20 (e^-1000/theta)^10 (1-e^-500/theta)^32 (e^-500/theta) ^24
theta = 707.3875
answer: 707.3875 + 500 = 1207.3875
How did they get the L(theta)? why is the deductible used as x? why do you add 500 at the end?
17. You are given:
1) Annual claim counts follow a Poisson distribution with mean lambda.
2) Lambda varies by insured. The distribution over all insureds is normal with mean 0.6 and variance is 0.04.
3) An insured is selected at random and claim counts over 3 years are simulated for this insured by first simulating lambda and then simulating each year's claim counts.
4) All simulations are done using the inversion method.
Uniform numbers in order : .28, .32, .13, .94
Determine the total number of simulated claims over three years.
lambda = 0.6 + inverse phi (.28) * rad .04 = .484
how did know to do that with lambda?
Any help would be greatly appreciated.
ASM PE2