Statistics of Extremes

Rating:
Summary: classic text of historical significance
Review: The asymptotic theory of extremes goes back to the work of Fisher and Tippett in 1928. Gnedenko in 1943 completed the theory for independent identically distributed random variables in his famous 1943 paper. However it was Emil Gumbel who popularized the technique in the 1950s most notable with the publication of this text in 1958. He showed engineers and scientists how to fit extreme value type distributions to reliability data. The double exponential distribution, the limiting distribution for Gaussian data is often referred to as the Gumbel distribution.

As a graduate student in the 1970s I studied extremes and the only available texts to rely on were Gumbel's book and the book on order statistics by David. Things changed shortly thereafter with the first edition of Galambos in 1978 and Leadbetter, Lindgren and Rootzen in 1983. These latter books extended the theory to dependent situations.

I found Gumbel's book somewhat difficult to read. He has a style that I found difficult to get use to and the mathematical language is not quite the same as the modern texts. Still it is an important classic text that researchers in extreme value theory should go through at least once.

If you are interested in learning about the theory and applications scratch it is best to go to the most recent modern text by Stuart Coles.

Rating:
Summary: classic text of historical significance
Review: The asymptotic theory of extremes goes back to the work of Fisher and Tippett in 1928. Gnedenko in 1943 completed the theory for independent identically distributed random variables in his famous 1943 paper. However it was Emil Gumbel who popularized the technique in the 1950s most notable with the publication of this text in 1958. He showed engineers and scientists how to fit extreme value type distributions to reliability data. The double exponential distribution, the limiting distribution for Gaussian data is often referred to as the Gumbel distribution.

As a graduate student in the 1970s I studied extremes and the only available texts to rely on were Gumbel's book and the book on order statistics by David. Things changed shortly thereafter with the first edition of Galambos in 1978 and Leadbetter, Lindgren and Rootzen in 1983. These latter books extended the theory to dependent situations.

I found Gumbel's book somewhat difficult to read. He has a style that I found difficult to get use to and the mathematical language is not quite the same as the modern texts. Still it is an important classic text that researchers in extreme value theory should go through at least once.

If you are interested in learning about the theory and applications scratch it is best to go to the most recent modern text by Stuart Coles.