AIMs: Describe the properties of distributions of operational loss data. Give a descriptive analysis of operational loss data. Describe ways to fit distributions to operational loss data. Carry out a threshold analysis of operational loss data. Describe how the aggregate loss distribution is developed.
Questions:
15.1. The authors (De Fontnouvelle et al) state "there is no commonly agreed-upon definition of what constitutes a heavy-tailed distribution. However, one such definition can be based upon a
distribution’s maximal moment ...In this paper, we will call a distribution light-tailed if it has finite moments of all orders, and heavy-tailed otherwise." According to this definition, which of the following distributions is heavy-tailed?
a. Weibull
b. Gamma
c. Type I Pareto (Power-law)
d. Lognormal
15.2. If an operational process fails whenever a sub-process fails, where the failure time of each sub-process is exponentially distributed, F(i), such that the total failure time is the sum of F(1) + F(2) + ... F(n), which distribution characterizes the total failure time (i.e., is the sum of exponentially distributed random variables)?
a. Weibull
b. Gamma
c. Type I Pareto (Power-law)
d. Lognormal
15.3. Extreme value theory suggests that which distribution is an appropriate choice for modeling loss severity under a thin-tailed assumption?
a. Exponential
b. Pareto
c. GPD
d. Loglogistic
Answers:
Questions:
15.1. The authors (De Fontnouvelle et al) state "there is no commonly agreed-upon definition of what constitutes a heavy-tailed distribution. However, one such definition can be based upon a
distribution’s maximal moment ...In this paper, we will call a distribution light-tailed if it has finite moments of all orders, and heavy-tailed otherwise." According to this definition, which of the following distributions is heavy-tailed?
a. Weibull
b. Gamma
c. Type I Pareto (Power-law)
d. Lognormal
15.2. If an operational process fails whenever a sub-process fails, where the failure time of each sub-process is exponentially distributed, F(i), such that the total failure time is the sum of F(1) + F(2) + ... F(n), which distribution characterizes the total failure time (i.e., is the sum of exponentially distributed random variables)?
a. Weibull
b. Gamma
c. Type I Pareto (Power-law)
d. Lognormal
15.3. Extreme value theory suggests that which distribution is an appropriate choice for modeling loss severity under a thin-tailed assumption?
a. Exponential
b. Pareto
c. GPD
d. Loglogistic
Answers:
