Sequence database searches require accurate estimation of the statistical significance of scores. Optimal local sequence alignment scores follow Gumbel distributions, but determining an important parameter of the distribution (lambda) requires time-consuming computational simulation. Moreover, optimal alignment scores are less powerful than probabilistic scores that integrate over alignment unc...

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...

Due to the advance computer technology, use of probability distributions has been raised up solve real life problems. These applications are found in reliability engineering, sciences, economics, psychology, survival analysis, and some others. This study offers a new model called Marshall–Olkin Extended Gumbel Type-II (MOEGT-II) which can various shapes failure rate function. The proposed distr...

We provide a combinatorial description of exclusion statistics in terms of minimal difference p partitions. We compute the probability distribution of the number of parts in a random minimal p partition. It is shown that the bosonic point p = 0 is a repulsive fixed point for which the limiting distribution has a Gumbel form. For all positive p the distribution is shown to be Gaussian. PACS numb...

MOTIVATION Background distribution statistics for profile-based sequence alignment algorithms cannot be calculated analytically, and hence such algorithms must resort to measuring the significance of an alignment score by assessing its location among a distribution of background alignment scores. The Gumbel parameters that describe this background distribution are usually pre-computed for a lim...

We investigate the statistics of the most connected node in scale-free networks. For a scale-free network model with homogeneous nodes, we show by means of extensive simulations that the exponential truncation, due to the finite size of the network, of the degree distribution governs the scaling of the extreme values and that the distribution of maxima follows the Gumbel statistics. For a scale...