TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2020W/HW04.3

Hurricane insurance

An insurance company needs to asses the risk associated with providing hurricane insurance. During 22 years from 1990 through 2011, Florida was hit by 27 major hurricanes (level 3 and above). The insurance company assumed Poisson distribution for modeling number of hurricanes.

(a)  If hurricanes are independent and the mean has not changed, what is the probability of having a year in Florida with each of the following?

1. No hits.
2. Exactly one hit.
3. More than two hits.

(b)  Use R to estimate the number of hurricane hits that will occur with the probability 99.5%.

Lösungsvorschlag von Friday

--Friday Sa 30 Jan 2021 16:44:02 CET

# Statistics and Probability HW #4
# Friday 
# Duedate: 02.11.2020

# Problem 3
# An insurance company needs to asses the risk associated with providing 
# hurricane insurance. During 22 years from 1990 through 2011, Florida was hit 
# by 27 major hurricanes (level 3 and above). The insurance company assumed 
# Poisson distribution for modeling number of hurricanes.
prob = 27/22

# Problem 3a)
# If hurricanes are independent and the mean has not changed, what is the 
# probability of having a year in Florida with each of the following?
  # (1) No hits.
  # (2) Exactly one hit.
  # (3) More than two hits.
result_3a1 <- dpois(0, prob)
result_3a2 <- dpois(1, prob)
result_3a3 <- 1 - sum(dpois(0:2, prob))

# Problem 3b)
result_3b <- qpois(0.995, prob)
# So with a 99.5% probability there will be less than 2 huricans