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POWER SERIES DISTRIBUTIONS IN MATHEMATICAL STATISTICS AND APPLIED PROBABILITY.

机译：数学统计中的幂级数分布和应用的概率。

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摘要

Discrete distributions, such as the Poisson, having the property that their probability mass functions are proportional to the terms of certain power series functions, are called power series distributions (PSD's).;Under mild conditions, it is shown that every PSD corresponds to a counting process as well as to a birth process. The Poisson process is characterized as being the only renewal process in the class of PSD's. Weighted geometric models are examined and characterizations through the size-biased model of some PSD's are obtained using form-invariance with given displacement. The independent of X and Y in the additive damage model (Z,X,Y) is shown to be a characteristic property of the PSD's. Several basic properties of the series defining functions as well as mathematical operations on the series defining functions and their stochastic interpretations are examined.;The concepts of conjugate pairs (X,O), where X is a discrete rv and O is a continuous rv, are introduced. Their classifications and interrelations are discussed. Characterizations of some PSD's are obtained as unique conjugate pairs. A condition for a mixture on the series parameter of a PSD (having support on the non-negative integers) to be identifiable is given, and is used to characterize the gamma and the beta distributions. Finally, characterizations of the prior distributions through certain forms of the posterior estimate are obtained, and examples are given.;We study distribution theory relating PSD's to absolutely continuous distributions using interesting probabilistic arguments. The upper (lower) tail probabilities of the PSD's are given as lower (upper) tail probabilities of a family of absolutely continuous distributions. These tail probability relationships are extended to cases involving differences of independent rv's having PSD's and non-central absolutely continuous distributions. Monotonicity of the power functions of certain tests based on these non-central distributions with respect to nuisance and non-centrality parameters is considered.
机译：离散分布（例如Poisson）具有其概率质量函数与某些幂级数函数的项成比例的特性，被称为幂级数分布（PSD）。在温和条件下，表明每个PSD对应于一个计数过程以及出生过程。泊松过程是PSD类别中唯一的更新过程。使用给定位移的形式不变性，检查了加权几何模型，并通过一些PSD的尺寸偏置模型获得了特征。附加损害模型（Z，X，Y）中X和Y的独立性被证明是PSD的特征。研究了系列定义函数的几个基本属性以及对系列定义函数的数学运算及其随机性解释。共轭对（X，O）的概念，其中X是离散rv，O是连续rv，介绍。讨论了它们的分类和相互关系。一些PSD的特征作为唯一的共轭对获得。给出了PSD序列参数上的混合（支持非负整数）可识别的条件，并将其用于表征γ和β分布。最后，通过后验估计的某些形式获得了先验分布的特征，并给出了例子。我们使用有趣的概率论研究了将PSD与绝对连续分布相关的分布理论。 PSD的较高（较低）尾部概率作为绝对连续分布族的较低（较高）尾部概率给出。这些尾部概率关系扩展到涉及具有PSD和非中心绝对连续分布的独立rv的差异的情况。基于扰动和非中心性参数，考虑了基于这些非中心分布的某些测试的幂函数的单调性。

著录项

  • 作者

    ABDUL-RAZAK, RAFID SAEED.;

  • 作者单位

    The Pennsylvania State University.;

  • 授予单位 The Pennsylvania State University.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 1983
  • 页码 95 p.
  • 总页数 95
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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