Before I begin, please note: I hated this chapter. If there are any errors please let me know asap!
A deductible is an amount that is subtracted from an insurance claim. If you have a $500 deductible on your car insurance, your insurance company will only pay damages incurred beyond $500. We are interested in the following random variables: and .
- Payment per Loss:
- Limited Payment per Loss:
- For an exponential distribution,
- For a Pareto distribution,
- For a single parameter Pareto distribution,
- The random variable is said to be shifted by and censored.
- is called mean excess loss or mean residual life.
- The random variable can be called limited expected value, payment per loss with claims limit, and amount not paid due to deductible. can be called a claims limit or deductible depending on how it is used in the problem.
- If data is given for with observed values and number of observations or probabilities, the data is called the empirical distribution. Sometimes empirical distributions may be given for a problem, but you are still asked to assume an parametric distribution for .