Fluctuations of the maximal particle energy of the quantum ideal gas and random partitions Abstract We investigate the limiting distribution of the fluctuations of the maximal summand in a random partition of a large integer with respect to a multiplicative statistics. We show that for a big family of Gibbs measures on partitions (so called generalized Bose–Einstein statistics) this distributio...

In this paper, our objective is to test the statistical hypothesis : ( ) ( ) for all against : ( ) ( ) 1 H F x F x x H F x F x o o o = ≠ for some , x where ( ) F x o is a known distribution function. In this study, a goodness of fit test statistics for Gumbel distribution based on Kullback-Leibler information is studied. The performance of the test under simple random sampling is investigated u...

Abstract: This paper unifies and extends results on a class of multivariate Extreme Value (EV) models studied by Hougaard, Crowder, and Tawn. In these models both unconditional and conditional distributions are EV, and all lower-dimensional marginals and maxima belong to the class. This leads to substantial economies of understanding, analysis and prediction. One interpretation of the models is...

A spatially reconfigurable antenna arrays consists of an antenna array of finite length and fixed geometry which is displaced within a given area. Using these reconfigurable components, the performance of MIMO systems is remarkably improved by effectively positioning the array in its displacement area. This paper studies the large-system performance of MIMO setups with spatially reconfigurable ...

Pre-trained language models (PLMs) have recently enabled rapid progress on sentiment classification under the pre-train and fine-tune paradigm, where fine-tuning phase aims to transfer factual knowledge learned by PLMs classification. However, current methods ignore risk that cause problem of bias, is, tend inject positive or negative from contextual information certain entities (or aspects) in...

We study the extreme value distribution of stochastic processes modeled by superstatistics. Classical extreme value theory asserts that (under mild asymptotic independence assumptions) only three possible limit distributions are possible, namely: Gumbel, Fréchet and Weibull distribution. On the other hand, superstatistics contains three important universality classes, namely χ-superstatistics, ...

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...

A “semi-probabilistic” alignment algorithm which combines ideas from Smith-Waterman and probabilistic alignment is proposed and studied in detail. It is predicted that the score statistics of this “hybrid” algorithm is of the universal Gumbel form, with the key Gumbel parameter λ taking on a fixed asymptotic value for a wide variety of scoring parameters. We have also characterized the “extrema...

We study analytically the distribution of the minimum of a set of hierarchically correlated random variables E1, E2, . . ., EN where Ei represents the energy of the i-th path of a directed polymer on a Cayley tree. If the variables were uncorrelated, the minimum energy would have an asymptotic Gumbel distribution. We show that due to the hierarchical correlations, the forward tail of the distri...

Fluctuations of the maximal particle energy of the quantum ideal gas and random partitions Abstract We investigate the limiting distribution of the fluctuations of the maximal summand in a random partition of a large integer with respect to a multiplicative statistics. We show that for a big family of Gibbs measures on partitions (so called generalized Bose–Einstein statistics) this distributio...