Related papers: A Generalization of the Exponential-Poisson Distri…
Recently, it has been conjectured that the statistics of extremes is of relevance for a large class of correlated system. For certain probability densities this predicts the characteristic large $x$ fall-off behavior $f(x)\sim\exp (-a…
The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not…
Assuming an exponential power distribution is one way to deal with outliers in regression and clustering, which can increase the robustness of the analysis. Gaussian distribution is a special case of an exponential distribution. And an…
A one-dimensional Vlasov-Poisson system is considered to elucidate how the information entropies of the probability distribution functions of the electron position and velocity variables evolve in the Landau damping process. Considering the…
We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied…
The decay of a quasiparticle in an isolated quantum dot is considered. At relatively small time the probability to find the system in the initial state decays exponentially: $P(t)\sim \exp(-\Gamma t)$, in accordance with the golden rule.…
We consider a measure $\psi$ k of dispersion which extends the notion of Wilk's generalised variance, or entropy, for a d-dimensional distribution, and is based on the mean squared volume of simplices of dimension k $\le$ d formed by k + 1…
In regression analysis under artificial neural networks, the prediction performance depends on determining the appropriate weights between layers. As randomly initialized weights are updated during back-propagation using the gradient…
The first part of this work considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
When $S=(S_t)_{t\ge 0}$ is an $\alpha$-stable subordinator, the sequence of ordered jumps of $S$, up till time $1$, omitting the $r$ largest of them, and taken as proportions of their sum $^{(r)}S_t$, defines a 2-parameter distribution on…
Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions $\{p_k\}$ for situations in…
Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard…
Modern datasets are characterized by a large number of features that may conceal complex dependency structures. To deal with this type of data, dimensionality reduction techniques are essential. Numerous dimensionality reduction methods…
By comparing two expressions for the polarization function given in terms of two different local-field factors, G_+(q,iw) and G_s(q,iw), we have derived the kinetic-energy-fluctuation (or sixth-power) sum rule for the momentum distribution…
Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…
Bayesian binary regression is a prosperous area of research due to the computational challenges encountered by currently available methods either for high-dimensional settings or large datasets, or both. In the present work, we focus on the…
Nadarajah and Gupta (2004) introduced the beta Fr\'echet (BF) distribution, which is a generalization of the exponentiated Fr\'echet (EF) and Fr\'echet distributions, and obtained the probability density and cumulative distribution…
Stable distributions is an interesting and important class of probability distributions. They were discovered explicitly by Paul L\'{e}vy in 1925 \cite{lk}. They possess many interesting properties, most importantly they are by definiton…
We consider Shannon entropy, Fisher information, R\'enyi entropy, and Tsallis entropy to study the quantum droplet phase in Bose-Einstein condensates. In the beyond mean-field description, the Gross-Pitaevskii equation with Lee-Huang-Yang…