题目
Peter the Risk Analyst wants to characterize an operational loss severity process with a relatively simple and recognizable probability distribution. His first choice is the lognormal distribution. Peter has several criteria for his distribution. The lognormal distribution does support, or at least does not violate, each of the following criteria EXCEPT which of the following criteria is not met by the lognormal distribution?
选项
A.He requires a genuine probability distribution
B.His expected loss is non-negative and the standard deviation is significantly greater than one
C.He wants summation stability: his simulation will add several independent random variables and he wants their sum to maintain the same distribution
D.He wants positive skew (losses are positive values; aka, L\/P format) where the mean is greater than the median, and he does not want a theoretical limit on the maximum loss
答案
C
解析
While normal random variables satisfy summation stability, lognormal variables do not: the product of lognormals is lognormal, not the sum.In regard to (A), (B) and (D), each is TRUE about the lognormal distribution. It is a probability distribution with two paramaters, μ and σ. It has positive skew with asymptotic (infinite) upper bound, just as the normal is asymptotic on both sides. 尽管正态随机变量满足求和稳定性，但对数正态变量不满足：对数正态的乘积是对数正态，而不是求和是。 （A），（B）和（D）都是正确的。 它是具有两个参数μ和σ的概率分布。它具有正偏斜和渐近（无限）上界，就像正态在两边都是渐近的一样。