  In order to account for large variance and fat tail of damage by natural
disaster, we study a simple model by combining distributions of disaster and
population/property with their spatial correlation. We assume fat-tailed or
power-law distributions for disaster and population/property exposed to the
disaster, and a constant vulnerability for exposed population/property. Our
model suggests that the fat tail property of damage can be determined either by
that of disaster or by those of population/property depending on which tail is
fatter. It is also found that the spatial correlations of population/property
can enhance or reduce the variance of damage depending on how fat the tails of
population/property are. In case of tornadoes in the United States, we show
that the damage does have fat tail property. Our results support that the
standard cost-benefit analysis would not be reliable for social investment in
vulnerability reduction and disaster prevention.
