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Lecture

Gumbel Distribution: Properties and Illustrations

In course

COM-417: Advanced probability and applications

In this course, various aspects of probability theory are considered. The first part covers the main theorems in the field (law of large numbers, central limit theorem), while the second part focuses on the theory of martingales and concentration inequalit ...

Description

This lecture covers the properties of the Gumbel distribution, including the Erdös-Renyi proposition and its application in the coupon collector problem. The slides illustrate the concepts with examples and proofs, emphasizing the independence of events.

Instructors (2)

Olivier Lévêque

Olivier Lévêque was born in Switzerland in 1971. He received the physics diploma from EPFL in 1995 and completed his PhD in mathematics at EPFL in 2001. Since then, he has been with the Laboratory of Information Theory at EPFL. He spent the academical year 2005-2006 at the Electrical Engineering Department of Stanford University, where he was appointed as lecturer. His research interests include stochastic analysis, random matrices, wireless communications and information theory.

Yanina Yurina Shkel

Official source

Related concepts (11)

Gumbel distribution

In probability theory and statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions. This distribution might be used to represent the distribution of the maximum level of a river in a particular year if there was a list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur.

Generalized extreme value distribution

In probability theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel, Fréchet and Weibull families also known as type I, II and III extreme value distributions. By the extreme value theorem the GEV distribution is the only possible limit distribution of properly normalized maxima of a sequence of independent and identically distributed random variables.

Probability distribution fitting

Probability distribution fitting or simply distribution fitting is the fitting of a probability distribution to a series of data concerning the repeated measurement of a variable phenomenon. The aim of distribution fitting is to predict the probability or to forecast the frequency of occurrence of the magnitude of the phenomenon in a certain interval. There are many probability distributions (see list of probability distributions) of which some can be fitted more closely to the observed frequency of the data than others, depending on the characteristics of the phenomenon and of the distribution.

Fréchet distribution

The Fréchet distribution, also known as inverse Weibull distribution, is a special case of the generalized extreme value distribution. It has the cumulative distribution function where α > 0 is a shape parameter. It can be generalised to include a location parameter m (the minimum) and a scale parameter s > 0 with the cumulative distribution function Named for Maurice Fréchet who wrote a related paper in 1927, further work was done by Fisher and Tippett in 1928 and by Gumbel in 1958.

Id Tech

id Tech is a series of separate game engines designed and developed by id Software. Prior to the presentation of the id Tech 5-based game Rage in 2011, the engines lacked official designation and as such were simply referred to as the Doom and Quake engines, from the name of the main game series the engines had been developed for. "id Tech" has been released as free software under the GNU General Public License. id Tech versions 0 to 3 were released under GPL-2.0-or-later. id Tech versions 3.5 to 4.

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