ESTIMATING EXTREME-VALUE INDEX FROM RECORDS

1.IntroductionLet{X.,n21}beasequenceoflidry'swithanondegeneratedistributionfunctionF(x).Supposethereexistsomeconstantsan>0,b.6RandsomeacERsuchthatwhereG.standsforoneoftheextremevaluedistributions:Heretheindex7ERisarealparameter(interpret(1 box)--'/ryase--"for7~0).Theestimationoftheextreme-valueindex7isveryimportantbothintheextremevaluetheoryandinpractice.Manystatistics,suchasHillestimator(forcaseac>0),PickandsestimatorandDekkers-EinmahLdeHaan'smomentestimatorwhicharebasedonafinitesample,…     

基于队列式缓存结构的视频图像存储算法

针对视频图像数据实时存储过程中普遍存在的丢帧问题,通过深入分析典型的存储算法,找出实时存储过程中视频图像数据丢失的原因：计算机在连续存储相同大小的文件时,存储速度在一定的范围内波动.本文采用队列式缓存结构有效地消除了存储速度波动所带来的影响,保证了在数据流速小于磁盘平均存储速度的前提下,高速视频图像数据的实时存储,解决了丢帧问题.实践验证了该算法的可行性与可靠性.     

The expected payoff to Internet auctions

In an Internet auction, the expected payoff acts as a benchmark of the reasonableness of the price that is paid for the purchased item. Since the number of potential bidders is not observable, the expected payoff is difficult to estimate accurately. We approach this problem by considering the bids as a record and 2-record sequence of the potential bidder’s valuation and using the Extreme Value Theory models to model the tail distribution of the bidder’s valuation and study the expected payoff. Along the discussions for three different cases regarding the extreme value index γ, we show that the observed payoff does not act as an accurate estimation of the expected payoff in all the cases except a subclass of the case γ = 0. Within this subclass and under a second order condition, the observed payoff consistently converges to the expected payoff and the corresponding asymptotic normality holds.      

Bayesian inference using record values from Rayleigh model with application

In this article, based on a set of upper record values from a Rayleigh distribution, Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameter, and some lifetime parameters such as the reliability and hazard functions. Bayes estimators have been developed under symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. These estimators are derived using the informative and non-informative prior distributions for σ. We compare the performance of the presented Bayes estimators with known, non-Bayesian, estimators such as the maximum likelihood (ML) and the best linear unbiased (BLU) estimators. We show that Bayes estimators under the asymmetric loss functions are superior to both the ML and BLU estimators. The highest posterior density (HPD) intervals for the Rayleigh parameter and its reliability and hazard functions are presented. Also, Bayesian prediction intervals of the future record values are obtained and discussed. Finally, practical examples using real record values are given to illustrate the application of the results.     

Bayesian inference for Pr (Y

《Applied Mathematical Modelling》2014,38(5-6):1698-1709

Limit theorems for numbers of near-records

Observations occurring between successive record times and within a distance a > 0 of the current record value are called near-records. Limit theorems for the number ξ _n (a) of near records are found for cases in which the parent distribution lies in a maximal domain of attraction and a is a function of n. Corollaries are indicated for numbers of near-k-records and sums of near-records. If the parent law is thin-tailed and a is constant, then a centered and normed version of logξ _n (a) has a limit law under appropriate conditions.      

Invariance Principles for Paced Record Times and Applications

Let {Y_n:n0} be a sequence of independent and identically distributed random variables with continuous distribution function, and let {N(t):t0} be a point process. In this paper, making use of strong invariance principles, we establish limit laws for the paced record process {X(t):t0} based on {Y_n:n0} and {N(t):t0}. We consider as applications of our main results, the case of the classical and paced record models. We conclude by extensions of our theorems to non-homogeneous record processes.     

一类特殊Weibull分布纪录值之和的中心极限定理

给出了参数τ为正整数的倒数为Weibull分布纪录值之和的中心极限定理。     

Characterization of probability distributions by conditional expectation of function of record statistics

In this paper, two general classes of distributions have been characterized through conditional expectation of power of difference of two record statistics. Further, some particular cases and examples are also discussed.