Mathematical explanation
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Publicado: 9 de abril de 2011
MATHEMATICAL EXPLANATION
Losses depend on two random variables. The first is the number of losses that will occur in a specified period. For example, a healthy policyholder withhospital insurance will have no losses in most years, but in some years he could have one or more accidents or illnesses requiring hospitalization. This random variable for the number oflosses is commonly referred to as the frequency of loss and its probability distribution is called the frequency distribution. The second random variable is the amount of the loss,given that a loss has occurred. For example, the hospital charges for an overnight hospital stay would be much lower than the charges for an extended hospitalization. The amount of lossis often referred to as the severity and the probability distribution for the amount of loss is called the severity distribution. By combining the frequency distribution with theseverity distribution we can determine the overall loss distribution.
Example: Consider a car owner who has an 80% chance of no accidents in a year, a 20% chance of being in a singleaccident in a year, and no chance of being in more than one accident in a year. For simplicity, assume that there is a 50% probability that after the accident the car will need repairscosting 500, a 40% probability that the repairs will cost 5000, and a 10% probability that the car will need to be replaced, which will cost 15,000. Combining the frequency and severitydistributions forms the following distribution of the random variable X, loss due to accident
F(x) = .80 donde x= 0
F(x)=.10 donde x=500
F(x)=.08 donde x=5000
F(x)=.02donde x= 15000
Para lunes calcula la media aritmética de las observaciones. La varianza y la desviación Standard la calcularemos en clases traigan calculadora científica.
Losses depend on two random variables. The first is the number of losses that will occur in a specified period. For example, a healthy policyholder withhospital insurance will have no losses in most years, but in some years he could have one or more accidents or illnesses requiring hospitalization. This random variable for the number oflosses is commonly referred to as the frequency of loss and its probability distribution is called the frequency distribution. The second random variable is the amount of the loss,given that a loss has occurred. For example, the hospital charges for an overnight hospital stay would be much lower than the charges for an extended hospitalization. The amount of lossis often referred to as the severity and the probability distribution for the amount of loss is called the severity distribution. By combining the frequency distribution with theseverity distribution we can determine the overall loss distribution.
Example: Consider a car owner who has an 80% chance of no accidents in a year, a 20% chance of being in a singleaccident in a year, and no chance of being in more than one accident in a year. For simplicity, assume that there is a 50% probability that after the accident the car will need repairscosting 500, a 40% probability that the repairs will cost 5000, and a 10% probability that the car will need to be replaced, which will cost 15,000. Combining the frequency and severitydistributions forms the following distribution of the random variable X, loss due to accident
F(x) = .80 donde x= 0
F(x)=.10 donde x=500
F(x)=.08 donde x=5000
F(x)=.02donde x= 15000
Para lunes calcula la media aritmética de las observaciones. La varianza y la desviación Standard la calcularemos en clases traigan calculadora científica.
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