_{0}(X

_{0}/X)

^{α}, Gumbel and Fréchet distributions also show promise. Here P

_{0}is the probability that cumulative damage, x, is greater than a threshold value, X

_{0}, and P is the probability that x > X > X

_{0}. It is easily shown that when α < 1, the distribution has no well-defined mean, and when α < 2 there is no well-defined variance. Since the normalized damage time series seems to be stationary, fitting extreme value distributions can yield estimates of the probabilities of very rare events outside the experience embodied in the 1900-2008 record. If the counts of destructive seasons with losses > $34.5B, are binned temporally by decades, there is no statistical justification for questioning that they obey a Poisson distribution with rate = 1 per decade, as one would expect. Only two of the eleven devastating seasons occurred during the cool phase of the Atlantic Multidecadal Oscillation when hurricane activity is generally suppressed. This seeming bias is easily attributable to chance (Chi-square p = 13%).The fitted Pareto distribution extrapolates impacts with return periods of 200 yr, $304B; 500 yr, $592B; and 1000 yr, $980B. The 100 year event, $183B, is in reasonable agreement with the earlier estimates based upon compound log-normal distributions.

Nonetheless, there are reasons to question Pareto estimates. The extrapolation from 100 to 1000-yr return period extends far out on the unsampled tail. Although the log-log plotted exceedance probability curve becomes straighter at the end, it is still subtly concave downward. Moreover, the most extreme hurricanes should not exhibit the self-similarity property that is implicit in the Pareto formulation because their maximum intensity is constrained by thermodynamic MPI and size by the dynamic requirement for core Rossby number be >> 1.

Since none the three most destructive hurricanes so far (in 1900, 1926 and 2005) caused more than $170B in damage, unprecedented destruction would probably have to stem from multiple landfalls within the same season. For example, one might envision a repeat of 2005, where Katrina intensified east of Florida, devastated Miami and then followed the climatologically likely track to New Orleans. Then Rita destroyed Houston/Galveston, and Wilma hit Tampa Bay as a major flooding event. This scenario, whose probability can be assessed using a Bayesian tree, would result in single-season damage > $440B, the combined total from the Galveston Hurricane of 1900, the Miami Hurricane of 1926, the Havana-Tampa Hurricane of 1944. and Katrina extrapolated to 2008 coastal development and population. It is difficult to imagine a realistic scenario that would more than double this figure to $1000B. Still, examination hypothetical future disasters in this context promises insight into the worst possible hurricane scenarios.