Asymptotic Moments Research Articles

Novel two-parameter quadratic exponential distribution: Properties, simulation, and applications

This research paper introduces a novel two-parameter quadratic exponential distribution (NTPQED), thoroughly examining its statistical properties and practical applications. The study delves into essential characteristics of the distribution, including its asymptotic behavior, moments, order statistics, and entropies. Additionally, we present fuzzy reliability, value at risk, mean excess function, limited expected value function, tail value at risk, and tail variance. A comprehensive simulation study evaluates fifteen parameter estimation methods. To illustrate the practical relevance of the proposed distribution, three sets of real-world data are analyzed. The performance of the proposed distribution model is rigorously assessed using various model selection criteria and goodness-of-fit test statistics. Empirical findings consistently demonstrate the proposed distribution's superiority over existing models, highlighting its potential for multiple applications.

Induced magnetization in anisotropic environment

The non-Markovian dynamics of a two-dimensional charged harmonic oscillator linearly coupled to a neutral bosonic heat bath is investigated in a linear-polarized electric field. The analytical expressions for the time-dependent and asymptotic magnetic moment are derived for the Markovian and non-Markovian dynamics. It is predicted that the liner-polarized electric field generates strong orbital currents and magnetization in a symmetric harmonic oscillator embedded into anisotropic heat bath. The role of the mixed dissipative kernel in magnetization is analyzed.

Asymptotic moment stability of solutions to systems of nonlinear differential Itô equations with aftereffect

Asymptotic moment stability of solutions to systems of nonlinear differential Itô equations with aftereffect

The distribution of Manin’s iterated integrals of modular forms

Abstract We determine the asymptotic distribution of Manin’s iterated integrals of length at most 2. For all lengths, we compute all the asymptotic moments. We show that if the length is at least 3, these moments do in general not determine a unique distribution.

Scaling limit of the local time of random walks conditioned to stay positive

AbstractWe prove that the local time of random walks conditioned to stay positive converges to the corresponding local time of three-dimensional Bessel processes by proper scaling. Our proof is based on Tanaka’s pathwise construction for conditioned random walks and the derivation of asymptotics for mixed moments of the local time.

Two-parameter family of distributions: Properties, estimation, and applications

In this paper, a new flexible two-parameter family of distributions is introduced. Some mathematical properties, such as asymptotic behavior, moments, stochastic order, entropy, and quantile function, are examined. A special case of this family is introduced called Gemeay–Zeghdoudi distribution. The unknown parameters of the Gemeay–Zeghdoudi distribution are estimated via many estimators. The efficiency of the estimators is compared with a Monte Carlo simulation. The applicability of the new distribution is illustrated by the annual maximum flood and survival times of patients with breast cancer real data analyses.

Structure refinement and magnetic properties of synthetic Co[formula omitted]Ge[formula omitted]O[formula omitted](OH)[formula omitted] phyllogermanate

Co3Ge2O5(OH)4 relates to a specific group of 1:1 layered compounds with an ability to form either platy or tubular particles depending on chemical composition. Despite successful synthesis and perspective application, there is a lack of information on its crystal structure and magnetic properties, granted by Co ions. Co3Ge2O5(OH)4 phyllogermanate nanoparticles have been obtained using a hydrothermal method and characterised using powder X-ray diffraction and magnetisation measurements. Triclinic symmetry with a 1:P1 space group has been established. The unit cell contains three layers perpendicular to the c crystallographic direction, with 7.6 Å spacing and −b/3 shift of the middle layer. At a low magnetic field of 100 Oe the compound undergoes a magnetic transition at TN=5.2 K. The field of 9 T is not sufficient to take the sample to a magnetically saturated state with an asymptotic magnetic moment of 2.43 μB/Co2+. The estimations of the intralayer and interlayer exchange constants give values of J1/kB=2.75 K and J2/kB=0.25 K, respectively.

Moment Asymptotics of Population Size of Particles at Vertices for a Supercritical Branching Random Walk on a Periodic Graph

Moment Asymptotics of Population Size of Particles at Vertices for a Supercritical Branching Random Walk on a Periodic Graph

Asymptotic UMVUE: Asymptotic Moments Matching the UMVUE under the Ewens Sampling Formula

The Ewens sampling formula is a distribution related to the random partition of a positive integer. In this study, we investigate the issue of non-existent solutions in parameter estimation under the distribution. We derive the first and second moments matching estimators to the uniformly minimum variance unbiased estimator (UMVUE) in the asymptotic sense (hereafter referred to as Asymptotic UMUVE) using the Ewens sampling formula. A Monte Carlo simulation study is performed to evaluate the efficiency of the resulting estimators. AMS Subject Classification: 62F12, 62P25

Limit theory of sparse random geometric graphs in high dimensions

We study topological and geometric functionals of l∞-random geometric graphs on the high-dimensional torus in a sparse regime, where the expected number of neighbors decays exponentially in the dimension. More precisely, we establish moment asymptotics, functional central limit theorems and Poisson approximation theorems for certain functionals that are additive under disjoint unions of graphs. For instance, this includes simplex counts and Betti numbers of the Rips complex, as well as general subgraph counts of the random geometric graph. We also present multi-additive extensions that cover the case of persistent Betti numbers of the Rips complex.

Linearly immutable continuously time series modelled bivariate stochastic processes with vector values: Distinguishing features

Certain observations are assumed to be missed while studying finite continual extended Fourier transformations of time series with precisely stable (i+j) vector values. This is assumed to be the case. This is because the procedure requires studying extended finite Fourier transforms in a standardized manner. The goal is to get as close to an exact interpretation of the results as possible with the data at hand. The results will be put to use in decision-making, which is why this is being done. As a result of this new data, the continuously Fourier transformation will take a starring role in the findings. Asymptotic moments are currently receiving a lot of consideration from researchers all over the world. Case studies on the topic of electrical energy will be used to test our theoretical concepts.

SOME DISTINGUISHING CHARACTERISTICS OF THE LINEAR IMMUTABILITY OF CONTINUOUS TIME SERIES VIA BIVARIATE VECTOR VALUED STOCHASTIC PROCESSES

During the process of analyzing the continuous expanded finite Fourier transforms of strictly stable $(i+j)$ vector-valued time series, it is presumed that some of the observations have been misplaced. This is done on the basis of an assumption. This is due to the fact that the method entails looking at continuous extended finite Fourier transforms. This is done so that the findings can be interpreted in a manner that is as precise as is practical given the information that is available. The reason for this is so that the findings can be used to make better decisions. Consequently of this additional data, the continuous Fourier transform will become the focal point of the researchers' achievements. At the present time, the concept of asymptotic moments is garnering a large amount of interest from researchers all around the world. In this investigation we will apply our theoretical study in case study on the subject of Electricity Energy,

The hard-to-soft edge transition: Exponential moments, central limit theorems and rigidity

The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter α . For this point process, we obtain (1) exponential moment asymptotics, up to and including the constant term, (2) asymptotics for the expectation and variance of the counting function, (3) several central limit theorems and (4) a global rigidity upper bound.

Moment asymptotics of particle numbers at vertices for a supercritical branching random walk on a periodic graph

Рассматривается надкритическое симметричное ветвящееся случайное блуждание по многомерному графу с непрерывным временем и источниками генерации частиц, расположенными периодически. Получена логарифмическая асимптотика для моментов численностей частиц в каждой вершине графа при $t\to\infty$.

Parameter estimation of stochastic differential equation driven by small fractional noise

We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with the Hurst index . Under some assumptions on the drift coefficient, we obtain the asymptotic normality and moment convergence of maximum likelihood estimator of the drift parameter when a small dispersion coefficient .

Moment estimates for the exponential sum with higher divisor functions

We obtain asymptotic for the quantity $\int_0^1 \bigg|\sum_{n\le X}\tau_k(n)e(n\alpha)\bigg|d\alpha$ where $\tau_k(n) = \sum_{d_1\dots d_k = n} 1$. This follows from a quick application of the circle method. Along the way, we find minor arc bounds for the exponential sum with $\tau_k$, and asymptotics for high moments of the Dirichlet kernel.

Interpolating the stochastic heat and wave equations with time-independent noise: solvability and exact asymptotics

In this article, we study a class of stochastic partial differential equations with fractional differential operators subject to some time-independent multiplicative Gaussian noise. We derive sharp conditions, under which a unique global $$L^p(\Omega )$$ -solution exists for all $$p\ge 2$$ . In this case, we derive exact moment asymptotics following the same strategy as that in a recent work by Balan et al. (Inst Henri Poincaré Probab Stat. To appear, 2021). In the case when there exists only a local solution, we determine the precise deterministic time, $$T_2$$ , before which a unique $$L^2(\Omega )$$ -solution exists, but after which the series corresponding to the $$L^2(\Omega )$$ moment of the solution blows up. By properly choosing the parameters, results in this paper interpolate the known results for both stochastic heat and wave equations.

Asymptotic moments of spatial branching processes

Suppose that X =(X_t, tge 0) is either a superprocess or a branching Markov process on a general space E, with non-local branching mechanism and probabilities {mathbb {P}}_{delta _x}, when issued from a unit mass at xin E. For a general setting in which the first moment semigroup of X displays a Perron–Frobenius type behaviour, we show that, for kge 2 and any positive bounded measurable function f on E, limt→∞gk(t)Eδx[⟨f,Xt⟩k]=Ck(x,f),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\lim _{t\\rightarrow \\infty } g_k(t){\\mathbb {E}}_{\\delta _x}[\\langle f, X_t\\rangle ^k] = C_k(x, f), \\end{aligned}$$\\end{document}where the constant C_k(x, f) can be identified in terms of the principal right eigenfunction and left eigenmeasure and g_k(t) is an appropriate deterministic normalisation, which can be identified explicitly as either polynomial in t or exponential in t, depending on whether X is a critical, supercritical or subcritical process. The method we employ is extremely robust and we are able to extract similarly precise results that additionally give us the moment growth with time of int _0^t langle f, X_t rangle mathrm{d}s, for bounded measurable f on E.

Cohomology of the Universal Abelian Surface with Applications to Arithmetic Statistics

Abstract The moduli stack $\mathcal{A}_2$ of principally polarized abelian surfaces comes equipped with the universal abelian surface $\pi: \mathcal{X}_2 \to \mathcal{A}_2$. The fiber of π over a point corresponding to an abelian surface A in $\mathcal{A}_2$ is A itself. We determine the $\ell$-adic cohomology of $\mathcal{X}_2$ as a Galois representation. Similarly, we consider the bundles $\mathcal{X}_2^n \to \mathcal{A}_2$ and $\mathcal{X}_2^{\textrm{Sym}(n)} \to \mathcal{A}_2$ for all $n \geq 1$, where the fiber over a point corresponding to an abelian surface A is An and $\textrm{Sym}^n A$, respectively. We describe how to compute the $\ell$-adic cohomology of $\mathcal{X}_2^n$ and $\mathcal{X}_2^{\textrm{Sym}(n)}$ and explicitly calculate it in low degrees for all n and in all degrees for n = 2. These results yield new information regarding the arithmetic statistics on abelian surfaces, including an exact calculation of the expected value and variance as well as asymptotics for higher moments of the number of Fq-points.

Taylor’s law of fluctuation scaling for semivariances and higher moments of heavy-tailed data

We generalize Taylor's law for the variance of light-tailed distributions to many sample statistics of heavy-tailed distributions with tail index α in (0, 1), which have infinite mean. We show that, as the sample size increases, the sample upper and lower semivariances, the sample higher moments, the skewness, and the kurtosis of a random sample from such a law increase asymptotically in direct proportion to a power of the sample mean. Specifically, the lower sample semivariance asymptotically scales in proportion to the sample mean raised to the power 2, while the upper sample semivariance asymptotically scales in proportion to the sample mean raised to the power [Formula: see text] The local upper sample semivariance (counting only observations that exceed the sample mean) asymptotically scales in proportion to the sample mean raised to the power [Formula: see text] These and additional scaling laws characterize the asymptotic behavior of commonly used measures of the risk-adjusted performance of investments, such as the Sortino ratio, the Sharpe ratio, the Omega index, the upside potential ratio, and the Farinelli-Tibiletti ratio, when returns follow a heavy-tailed nonnegative distribution. Such power-law scaling relationships are known in ecology as Taylor's law and in physics as fluctuation scaling. We find the asymptotic distribution and moments of the number of observations exceeding the sample mean. We propose estimators of α based on these scaling laws and the number of observations exceeding the sample mean and compare these estimators with some prior estimators of α.