Related papers: Various New Inequalities for Beta Distributions
Many issues combine for consideration when speaking of Bell's Inequalities: nonlocality, realism, hidden variables, incompatible measures, wave function collapse, other. Each of these issues then may be viewed from several viewpoints:…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
In this paper, some new Gronwall type inequalities involving iterated integrals are given.
The work approaches the study of the fluctuations for the thermodynamic systems in the presence of the fields. The approach is of phenomenological nature and developed in a Gaussian approximation. The study is exemplified on the cases of a…
A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…
The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.
Some new inequalities of Karamata type are established with a convex function in this paper. The methods of our proof allow us to obtain an extended version of the reverse of Jensen inequality given by Pe{\v} cari\'c and Mi\'ci\'c. Applying…
The aim of this paper is to establish Hoeffding and Bernstein type concentration inequalities for weighted sums of exchangeable random variables. A special case is the i.i.d. setting, where random variables are sampled independently from…
This article proposes a new method of truncated estimation to estimate the tail index $\alpha$ of the extremely heavy-tailed distribution with infinite mean or variance. We not only present two truncated estimators $\hat{\alpha}$ and…
In the present paper we establish some new integral inequalities analogous to the well known Hadamard inequality by using a fairly elementary analysis.
In the paper, by using Lupa\c{s} integral inequality, the authors find some new inequalities for the complete elliptic integrals of the first and second kinds. These results improve some known inequalities.
Gaussian random vectors exhibit the loss of dimension phenomena, which relate to their joint survival tail behaviour. Besides, the fact that the components of such vectors are light-tailed complicates the approximations of various…
Two kinds of novel generalizations of Nesbitt's inequality are explored in various cases regarding dimensions and parameters in this article. Some other cases are also discussed elaborately by using the semiconcave-semiconvex theorem. The…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…
This paper presents an improved exponential tail bound for Beta distributions, refining a result in [15]. This improvement is achieved by interpreting their bound as a regular Kullback-Leibler (KL) divergence one, while introducing a…
In this paper, new sharpened Huygens type inequalities involving Bessel and modified Bessel functions of the first kinds are established
We estimate up to universal constants tails of symmetric and totally asymmetric 1-dimensional $\alpha$-stable distributions in terms of functions of the parameters of these distributions. In particular, for values of $\alpha$ close to $2$…
A transformation group approach to the prior for the parameters of the beta distribution is suggested which accounts for finite sets of data by imposing a limit to the range of parameter values under consideration. The relationship between…
Time series regression models are commonly used in time series analysis. However, in modern real-world applications, serially correlated data with an ultra-high dimension and fat tails are prevalent. This presents a challenge in developing…