1.1 Two simulations of the Smith model with different Σ matrices. Left panel: σ 11 = σ 22 = 9/8 and σ 12 = 0. Right panel: σ 11 = σ 22 = 9/8 and σ 12 = 1. The max-stable processes are transformed to unit Gumbel margins for viewing purposes.. 6 1.2 Plots of the Whittle–Matérn, the powered exponential, the Cauchy and the Bessel correlation functions-from left to right. The sill and the range para...

BACKGROUND The spatial and space-time scan statistics are commonly applied for the detection of geographical disease clusters. Monte Carlo hypothesis testing is typically used to test whether the geographical clusters are statistically significant as there is no known way to calculate the null distribution analytically. In Monte Carlo hypothesis testing, simulated random data are generated mult...

Recently, Rodríguez-Lallena and´Ubeda-Flores [8] have introduced a class of bivariate copulas which generalizes some known families such as the Farlie-Gumbel-Morgenstern distributions. In this paper we present multivariate generalizations of this class studying symmetry and dependence concepts, measuring the dependence among the components of each class, and providing several examples.

In this paper, with optimal normalized constants, the asymptotic expansions of the distribution of the normalized maxima from generalized Maxwell distribution is derived. It shows that the convergence rate of the normalized maxima to the Gumbel extreme value distribution is proportional to 1/ log n.

We develop a general method for computing extreme value distribution (Gumbel, 1958) parameters for gapped alignments. Our approach uses mixture distribution theory to obtain associated BLOSUM matrices for gapped alignments, which in turn are used for determining significance of gapped alignment scores for pairs of biological sequences. We compare our results with parameters already obtained in ...

In this paper, the concomitants of case-II of generalized order statistics from Farlie-Gumbel-Morgenstern (FGM) distributions and recurrence relations between their moments are studied. Further, we provide the minimum variance linear unbiased estimator of the location and scale parameters of the concomitants of ordinary order statistics from some distributions.

We consider a generalization of the bivariate Farlie-Gumbel-Morgenstern (FGM) distribution by introducing additional parameters. For the generalized FGM distribution, the admissible range of the association parameter allowing positive quadrant dependence property is shown. Distributional properties of concomitants for this generalized FGM distribution are studied. Recurrence relations between m...

We investigate the maximal non-critical cluster in a big box in various percolation-type models. We investigate its typical size, and the fluctuations around this typical size. The limit law of these fluctuations are related to maxima of independent random variable with law described by a single cluster. Key-words: Maximal clusters, exponential law, Gumbel distribution, FKG inequality, second m...

We discuss tail behaviors, subexponentiality and extreme value distribution of logarithmic skew-normal random variables. With optimal normalized constants, the asymptotic expansion of the distribution of the normalized maximum of logarithmic skew-normal random variables is derived. It shows that the convergence rate of the distribution of the normalized maximum to the Gumbel extreme value distr...