WOLFRAM|DEMONSTRATIONS PROJECT

Tail Conditional Expectations

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distribution
GeneralizedParetoDistribution
LogNormalDistribution
GammaDistribution
WeibullDistribution
β
ξ
β
0.5
ξ
0.5
PDF of distribution
2.
3.
(1.x+1)
return period
return period in years
50.
probability of return each year (α)
0.02000
visualize
probability density function
cumulative density function
In modeling catastrophes, it is often useful to know how large a loss can be expected to be, given the assumption that the loss is greater than some amount. This value—the so-called "tail conditional expectation"—may be of great relevance to those who insure or reinsure against the highest levels of losses; it is sometimes what is meant by the actuarial term "probable maximum loss". In this Demonstration, you select a family of distributions and two parameters that instantiate a particular distribution from that family. The resulting distribution determines the probability that a loss from some catastrophe will exceed some amount. You can then set the magnitude of the catastrophe you wish to study. A "return period" of 50, for example, means that you wish to study catastrophes that are larger than all of those that will, on average, occur over a 50 year period. The Demonstration responds by drawing the distribution you have selected (you select whether you want to see the probability density function or the cumulative density function): the red dashed line shows the "exceedance value" and the blue line shows the tail conditional expectation, which is computed using numerical integration. An inset grid recapitulates the results.