Extreme Value Distributions and Their Applications

Extreme Value Distributions are the limiting distributions of the normalized maximum or minimum of a very large number of independent random variables from the same distribution. Fisher and Tippett (1928) showed that maximum of a sample independent and identically distribution(iid) after proper normalization converges in distribution to one of the three possible distribution, the Gumbel distribution, the Frechet distribution and the Weibull distribution. The same is true for the minimum of a sample from an iid. These three distributions are special cases of generalized extreme value distribution. In this talk some distributional properties of these distributions will be presented