Background about extreme value distribution

In class we are discussing the statistical parameters surrounding BLAST sequence searches. The BLAST scores fit an extreme value distribution. There are three types: the Gumbel is of most interest to us. Extreme value distribution is a branch of statistics that deals with predicting values _extremely_ different than the median. It has been shown empirically that extreme value distributions have better predictive powers for rare events than other distributions, such as the normal distribution. Here's some information I found about extreme value distributions in other contexts:

The washer factory:

Background of the Generalized Extreme Value Distribution

Like the extreme value distribution, the generalized extreme value distribution is often used to model the smallest or largest value among a large set of independent, identically distributed random values representing measurements or observations. For example, you might have batches of 1000 washers from a manufacturing process. If you record the size of the largest washer in each batch, the data are known as block maxima (or minima if you record the smallest). You can use the generalized extreme value distribution as a model for those block maxima.

The generalized extreme value combines three simpler distributions into a single form, allowing a continuous range of possible shapes that includes all three of the simpler distributions. You can use any one of those distributions to model a particular dataset of block maxima. The generalized extreme value distribution allows you to "let the data decide" which distribution is appropriate.

Size of a 100-year flood

A one-hundred year flood is calculated to be the maximum level of flood water to be expected in an average one-hundred-year period. Sometimes, a 500-year or 10,000-year flood is also calculated (especially, in low lying countries, such as the Netherlands). The 100-year flood is sometimes referred to as the 1% flood, since there is a 1% chance of it occurring in any year. Based on the expected water level, an expected area of inundation may be mapped out according to elevation above sea level. This area figures very importantly in building permits, environmental regulations, and flood insurance.

The mathematical field of extreme value theory was created to model rare events such as 100-year floods for the purposes of civil engineering.

Wikipedia entry has good links, too