S-Type Risk Function

Assuming a Gamma distribution for the occurrence function and a quadratic form for the impact function (Equation 7.7), the final S-type risk function will be as follows. 

Equation 7.10 is used to calculate the maximum loss with respect to a given confidence level a, i.e., decision maker provides a confidence level a and plug it in Equation 7.10 to determine the maximum dollar loss due to the MtT type event. 

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As mentioned in Section 7.10, Gamma distribution can be used to model the S-type occurrence function. Combining the impact and occurrence functions, we obtain the following S-type risk function (see Yang (2006) for the calculations of other types of risks functions). 

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