相关论文: Hypergeometric tail inequalities: ending the insan…

We present a generic and powerful approach to study the statistics of extreme phenomena (meteorology, finance, biology...) that we apply to the statistical estimation of the tail of the distribution of earthquake sizes. The chief innovation…

Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…

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…

Asymptotic theory of tail index estimation has been studied extensively in the frequentist literature on extreme values, but rarely in the Bayesian context. We investigate whether popular Bayesian kernel mixture models are able to support…

General hypergeometric distribution (GHGD) definition: from a finite space $N$ containing $n$ elements, randomly select totally $T$ subsets $M_i$ (each contains $m_i$ elements, $1 \geq i \geq T$), what is the probability that exactly $x$…

In this note we prove an inequality for t-geometric means that immediately implies the recent results of Audenaert [2] and Hayajneh-Kittaneh [6].

In extreme value inference it is a fundamental problem how the target value is required to be extreme by the extreme value theory. In iid settings this study both theoretically and numerically compares tail estimators, which are based on…

We propose a mean functional which exists for any probability distributions, and which characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in sharp contrast to the mean excess plot which…

We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…

Survey of hypergeometric motives, with a focus on their source varieties, Hodge numbers, and L-functions.

For $n$ positive numbers ($a_k$, $1\leq k \leq n$), enhanced inequalities about the arithmetic mean ($A_n \equiv \frac{\sum_ka_k}{n}$) and the geometric mean ($G_n\equiv \sqrt[n]{\Pi_ka_k}$) are found if some numbers are known, namely,…

In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.

We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the…

We study the upper tail of the number of arithmetic progressions of a given length in a random subset of {1,...,n}, establishing exponential bounds which are best possible up to constant factors in the exponent. The proof also extends to…

The discrete isoperimetric inequality states that among all n -gons with a fixed area, the regular n -gon has the least perimeter. We prove analogues of the discrete isoperimetric inequality (involving circumradius or inradius) for cyclic…

Consider the upper tail probability that the homomorphism count of a fixed graph $H$ within a large sparse random graph $G_n$ exceeds its expected value by a fixed factor $1+\delta$. Going beyond the Erd\H{o}s-R\'enyi model, we establish…

In this paper non-asymptotic exponential estimates are derived for the tail distribution of polynomial martingale differences in terms unconditional tails distributions of summands. Applications are considered in the theory of polynomials…

(The third edition corrects minor typos and adds 3 chapters synthesized from published papers plus an appendix on maximum entropy distributions.) The monograph investigates the misapplication of conventional statistical techniques to fat…

We consider an inhomogeneous Erd\H{o}s-R\'enyi random graph ensemble with exponentially decaying random disconnection probabilities determined by an i.i.d. field of variables with heavy tails and infinite mean associated to the vertices of…

We find two-sided inequalities for the generalized hypergeometric function of the form ${_{q+1}}F_{q}(-x)$ with positive parameters restricted by certain additional conditions. Both lower and upper bounds agree with the value of…