Based on our analysis of the hopcount of the shortest path between two arbitrary nodes in the class Gp(N) of random graphs, the corresponding ßooding time is investigated. The ßooding time TN(p) is the minimum time needed to reach all other nodes from one node. We show that, after scaling, the ßooding time TN(p) converges in distribution to the two-fold convolution Λ(2∗) of the Gumbel distribut...

In probability theory and statistics, the generalized extreme value distribution (GEV) 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. Its importance arises from the fact that it is the limit distribution of the maxima of a sequence of indep...

Let {Xi, i = 1, 2, . . .} be i.i.d. standard gaussian variables. Let Sn = X1 + . . . + Xn be the sequence of partial sums and Ln = max 0≤i<j≤n Sj − Si √ j − i . We show that the distribution of Ln, appropriately normalized, converges as n → ∞ to the Gumbel distribution. In some sense, the the random variable Ln, being the maximum of n(n+1)/2 dependent standard gaussian variables, behaves like t...

APPENDIX: Lost Relatives of the Gumbel Trick Here we provide proofs for the results stated in the main text, together with additional supporting lemmas required for these proofs. A. Comparison of Gumbel and Exponential tricks In Section 2.3.1 we analyzed the asymptotic efficiency of different estimators of Z by measuring their asymptotic variance. (As all our estimators in the full-rank perturb...

By using the independence structure of points following a determinantal point process, we study the radii of the spherical ensemble, the truncation of the circular unitary ensemble and the product ensemble with parameter n and k. The limiting distributions of the three radii are obtained. They are not the Tracy-Widom distribution. In particular, for the product ensemble, we show that the limiti...

Using an associated branching process as the basis of our approximation, we show that typical inter-point distances in a multi-type random intersection graph have a defective distribution, which is well described by a mixture of translated and scaled Gumbel distributions, the missing mass corresponding to the event that the vertices are not in the same component of the graph. © 2010 Wiley Perio...

Several computer algorithms now exist for discovering multiple motifs (expressed as weight matrices) that characterize a family of protein sequences known to be homologous. This paper describes a method for performing similarity searches of protein sequence databases using such a group of motifs. By simultaneously using all the motifs that characterize a protein family, the sensitivity and spec...

By assuming that the underlying distribution belongs to the domain of attraction of an extreme value distribution, one can extrapolate the data to a far tail region so that a rare event can be predicted. However, when the distribution is in the domain of attraction of a Gumbel distribution, the extrapolation is quite limited generally in comparison with a heavy tailed distribution. In view of t...

This work presents a validation of wave parameters from the new sixty years Downscaled Ocean Waves (DOW) reanalysis database. This study compares quantiles of the Gumbel distribution of Hs (significant wave height) and Tp (peak period) from simulated data with an 11 months' time series obtained from a buoy moored seaward on the Santa Catarina coast. Analysis by means of Gumbel distribution quan...

Heterogeneity of economic agents is emphasized in a new trend of macroeconomics. Accordingly the new emerging discipline requires one to replace the production function, one of key ideas in the conventional economics, by an alternative which can take an explicit account of distribution of firms’ production activities. In this paper we propose a new idea referred to as production copula; a copul...