We study the asymptotic behavior of the diameter or maximum interpoint distance of a cloud of i.i.d. d-dimensional random vectors when the number of points in the cloud tends to infinity. This is a non standard extreme value problem since the diameter is a max U -statistic, hence the maximum of dependent random variables. Therefore, the limiting distributions may not be extreme value distributi...

In order to evaluate the importance of higher-order correlations in neural spike count codes, flexible statistical models of dependent multivariate spike counts are required. Copula families, parametric multivariate distributions that represent dependencies, can be applied to construct such models. We introduce the Frank mixture family as a new copula family that has separate parameters for all...

Assessing the significance of alignment scores of optimally aligned DNA or amino acid sequences can be achieved via the knowledge of the score distribution of random sequences. But this requires obtaining the distribution in the biologically relevant high-scoring region, where the probabilities are exponentially small. For gapless local alignments of infinitely long sequences this distribution ...

An asymptotic expansion is developed for the joint density of the sum and maximum of an i.i.d. sequence when the parent distribution is in the domain of extreme value attraction of the Gumbel distribution. Previous results by Chow and Teugels, extended by Anderson and Turkman, show that in this situation, the normalized sum and normalized maximum of the sample converge to independent normal and...

The Gumbel mixture model is a popular tool for modeling extreme events with mixed formation mechanisms. lack of shape parameter in the distribution makes it somewhat less practical compared to Weibull distribution, which widely used structural reliability and safety applications. Since has two forms (i.e., left- right-skewed), we describe as three-parameter distribution. additional ξ ∈ { − 1 , ...

In this paper, an approximation of the asymptotic of the distribution for maximum and minimum of the degree sequence defined over a random graph is determined using a new approach in terms of the Gumbel distribution for extremes.

We study a stochastic model of infection spreading on a network. At each time step a node is chosen at random, along with one of its neighbors. If the node is infected and the neighbor is susceptible, the neighbor becomes infected. How many time steps T does it take to completely infect a network of N nodes, starting from a single infected node? An analogy to the classic "coupon collector" prob...

The opinions expressed and conclusions reached by the authors are their own and do not represent any official position or opinion of the sponsoring organizations or their members. The sponsoring organizations make no representation or warranty to the accuracy of the information. Abstract. Copulas with a full-range tail dependence property can cover the widest range of positive dependence in the...