关于Papathanasiou的协方差展开式

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Marie Ernst, G. Reinert, Yvik Swan
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引用次数: 0

摘要

。本文给出了拉格朗日恒等式的一个概率表示,用它可以得到任意阶的papathanasiou型方差展开式。我们的展开得到了广义的权重序列,它依赖于任意选择的(非递减的)测试函数序列。该展开式适用于弱假设下的单变量目标分布,尤其适用于连续分布和格分布。在测试函数或底层分布的不同假设集下研究权重。提供了许多标准概率分布的具体示例(包括Pearson, Ord, Laplace, Rayleigh, Cauchy和Levy分布)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On Papathanasiou’s covariance expansions
. In this paper we provide a probabilistic representation of Lagrange’s identity which we use to obtain Papathanasiou-type variance expansions of arbitrary order. Our expansions lead to generalized sequences of weights which depend on an arbitrarily chosen sequence of (non-decreasing) test functions. The expansions hold for univariate target distribution under weak assumptions, in particular they hold for continuous and lattice distributions alike. The weights are studied under different sets of assumptions either on the test functions or on the underlying distributions. Many concrete illustrations for standard probability distributions are provided (including Pearson, Ord, Laplace, Rayleigh, Cauchy, and Levy distributions).
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
48
期刊介绍: ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.
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