柯西不等式的改进

对柯西不等式的一个改进下界作了进一步推广 ,并给出了它的若干应用例子     

D-efficient window experimental designs

In the paper we present a new method of calculating sampling intervals, so-called windows, allowing an experimenter some flexibility in timing the sample collection, while a minimum required design efficiency for parameter estimation is assured. The method is based on the Equivalence Theorem for D-optimality what makes the length of each window related to the parameter sensitivities. An example of calculating the windows in a pharmacokinetic study is presented. Some other methods of calculating efficient sampling windows are briefly discussed.     

Jensen不等式在导出和证明几何不等式中的应用

本文给出 Jensen 不等式在导出和证明几何不等式中的应用,揭示出一些几何不等式的来历及寻求证明的技巧。     

Improved approaches to interval estimation of effective doses for a logistic dose-response curve

Asymptotic confidence (delta) intervals and intervals based upon the use of Fieller's theorem are alternative methods for constructing intervals for the <$>\gamma<$>% effective doses (ED<$>_\gamma<$>). Sitter and Wu (1993) provided a comparison of the two approaches for the ED<$>_{50}<$>, for the case in which a logistic dose response curve is assumed. They showed that the Fieller intervals are generally superior. In this paper, we introduce two new families of intervals, both of which include the delta and Fieller intervals as special cases. In addition we consider interval estimation of the ED<$>_{90}<$> as well as the ED<$>_{50}<$>. We provide a comparison of the various methods for the problem of constructing a confidence interval for the ED<$>_\gamma<$>.     

The Poisson-X family of distributions

ABSTRACT

Recently, Risti? and Nadarajah [A new lifetime distribution. J Stat Comput Simul. 2014;84:135–150] introduced the Poisson generated family of distributions and investigated the properties of a special case named the exponentiated-exponential Poisson distribution. In this paper, we study general mathematical properties of the Poisson-X family in the context of the T-X family of distributions pioneered by Alzaatreh et al. [A new method for generating families of continuous distributions. Metron. 2013;71:63–79], which include quantile, shapes of the density and hazard rate functions, asymptotics and Shannon entropy. We obtain a useful linear representation of the family density and explicit expressions for the ordinary and incomplete moments, mean deviations and generating function. One special lifetime model called the Poisson power-Cauchy is defined and some of its properties are investigated. This model can have flexible hazard rate shapes such as increasing, decreasing, bathtub and upside-down bathtub. The method of maximum likelihood is used to estimate the model parameters. We illustrate the flexibility of the new distribution by means of three applications to real life data sets.     

A surplus process involving a compound Poisson counting process and applications

Abstract

In this paper, we introduce a surplus process involving a compound Poisson counting process, which is a generalization of the classical ruin model where the claim-counting process is a homogeneous Poisson process. The incentive is to model batch arrival of claims using a counting process that is based on a compound distribution. This reduces the difficulty of modeling claim amounts and is consistent with industrial data. Recursive formula, some properties and relevant main ruin theory results are provided. Further, we consider applications involving zero-truncated negative binomial and zero-truncated binomial batch arrivals when the claim amounts follow exponential or Erlang distribution.     

关于留数定理的一个推广

研究了留数定理的有关问题,通过举例论证和归纳推理等证明方法,得到了单个留数定理的一个推广结论,最后将此结论应用于一些积分问题中.     

科斯定理与国家理论——权力、可信承诺与政治企业家

权力与可信承诺是国家理论的核心问题。引入权力因素导致科斯定理不再成立:在交易成本为零时,权力的不可转让性消除了趋向最优谈判的压力;而有限承诺加大了谈判结果偏离帕累托最优效率的程度。因此,为了有助于理解经济增长和制度变迁的国家理论,需要分析那些拥有权力的个体的行为。这些人包括专制国家中的君主以及民主国家中的政治家和官僚等。在经济增长和制度变迁过程中,他们中的一些人扮演着政治企业家的角色,发挥着关键行动者和“第一行动集团”的作用。权力和可信承诺是政治企业家理论的重要构成要素,对于把握政治企业家和制度变迁的关系具有重要意义。     

A note on the Cauchy-type mixture distributions

An interesting class of continuous distributions, called Cauchy-type mixture, with potential applications in modelling erratic phenomena is introduced by Soltani and Tafakori [A class of continuous kernels and Cauchy type heavy tail distributions. Statist Probab Lett. 2013;83:1018–1027]. In this work, we provide more insights into the Cauchy-type mixture distributions, involving certain characterizations, connections with the generalized Linnik distributions and the class of discrete distributions induced by stable laws. We also prove that the Laplace transform of Cauchy-type mixture distributions when normalized by constant terms become as a density functions in terms of distributional conjugate property.     

Maximal Invariant and Weakly Equivariant Estimators

Equivariant functions can be useful for constructing of maximal invariant statistic. In this article, we discuss construction of maximal invariants based on a given weakly equivariant function under some additional conditions. The theory easily extends to the case of two or more weakly equivariant functions. Also, we derive a maximal invariant statistic when the group contains a sharply transitive and a characteristic subgroup. Finally, we consider the independence of invariant and weakly equivariant functions under some special conditions.