相关论文: Generalized factorial moments
Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions, due to…
In this paper, we investigate the stochastic counterpart of the generalized Wright analysis introduced in Beghin et al.~ in Integral Equations and Operator Theory, {\bf 97}, 2025. We define a new class of non-Gaussian and non-Markovian…
Factorial moments are convenient tools in nuclear physics to characterize the multiplicity distributions when phase-space resolution ($\Delta$) becomes small. For uncorrelated particle production within $\Delta$, Gaussian statistics holds…
Let $\mu$ be a positive measure on the real line with locally finite support $\Lambda$ and integer masses such that its Fourier transform in the sense of distributions is a purely point measure. An explicit form is found for an entire…
These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
We introduce generalized filtration with which we can represent situations such as some agents forget information at some specific time. The filtration is defined as a functor to a category Prob whose objects are all probability spaces and…
We introduce semicontinuous summation methods for series of fuzzy numbers and give Tauberian conditions under which summation of a series of fuzzy numbers via generalized Dirichlet series and via generalized factorial series implies its…
In this note, we consider the performance of the classic method of moments for parameter estimation of symmetric variance-gamma (generalized Laplace) distributions. We do this through both theoretical analysis (multivariate delta method)…
Many modern applications collect data that comes in federated spirit, with data kept locally and undisclosed. Till date, most insight into the causal inference requires data to be stored in a central repository. We present a novel framework…
In this article, we study the distribution of index of Farey fractions which was first introduced and studied by Hall and Shiu. We provide asymptotic formulas for moments of index of Farey fractions twisted by Dirichlet characters for Farey…
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the…
It is demonstrated that the "generalized fluctuation-dissipation theorem" [Physica A 106, 443 (1981)] covers the later suggested "fluctuation theorems" and related statistical equalities.
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
In this article, we consider an imputation method to handle missing response values based on semiparametric quantile regression estimation. In the proposed method, the missing response values are generated using the estimated conditional…
We investigate the properties of the moments of the cot function using the central factorial numbers. Using a new integral representation of the central factorial numbers, we find a new way to express these moments in terms of recursive…
Several convenient methods for calculation of fractional absolute moments are given with application to heavy tailed distributions. We use techniques of fractional differentiation to obtain formulae for $E[|X-\mu|^\gamma]$ with $1<\gamma<2$…
The Phi-measure of event-by-event fluctuations in high-energy heavy-ion collisions corresponds to the second moment of the fluctuating quantity distribution of interest. It is shown that the measure based on the third moment preserves the…
We derive a simple expression for the $r^{th}$ factorial moment $\mu_{(r)}$ of the geometric distribution of order $k$ with success parameter $p\in(0,1)$ (and $q=1-p$) in terms of its probability mass function $f_k(n)$. Specifically,…
Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law…