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By using the theory of the second-order regular variation, we study the rates of the weak convergence of the maximum order
statistics under power normalization. The exact rates are obtained in the uniform metric and the total variation metric. The
relationship between the rates of convergence under linear and under power normalization is derived. Some illustrative examples
are given for comparing the rates of convergence. 相似文献
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H.M. Barakat 《Journal of the Korean Statistical Society》2012,41(3):369-374
The class of limit distribution functions of the random record model is fully characterized. Necessary and sufficient conditions as well as the domains of attraction of the limit distribution functions are obtained. 相似文献
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In this paper the work of Pancheva (1984) for extreme order statistics under nonlinear normalization is extended to order statistics with variable ranks. Two new results are proved. The first is that under nonlinear normalization, the nondegenerate type (family of types) of the distribution functions with two finite growth points is a possible weak limit of any central order statistic with regular rank sequence. The second result is that the possible nondegenerate weak limits of any central order statistic with regular rank under the traditionally linear normalization and under the power normalization are the same. Finally, the class of all possible weak limits for lower and upper intermediate order statistics is derived under power normalization from the corresponding weak limits of extremes under power normalization. 相似文献
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This article presents a review and comparison of the most important expanded families of distributions. We set the essential requirements by which an expanding family can fit any dataset successfully. A new method is proposed to construct families, which fulfill these essential requirements. Consequently, two families are suggested, which are more tractable than many other known families and possess very wide range of the indices of skewness and kurtosis. The article is motivated by two applications to real dataset. 相似文献
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H. M. Barakat 《Statistics》2013,47(5):1005-1012
In this paper, we show that both the class of beta-generated distributions GF and its base distribution F belong to the same domain of maximal (or minimal or upper record value or lower record value) attraction. Moreover, it is shown that the weak convergence of any non-extreme order statistic (central or intermediate order statistic), based on a base distribution F, to a non-degenerate limit type implies the weak convergence of GF to a non-degenerate limit type. The relations between the two limit types are deduced. 相似文献
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H. M. Barakat 《统计学通讯:理论与方法》2013,42(11):1985-1992
In this article, by using the dropping argument, a general recurrence relation satisfied by the joint cumulative distribution functions of order statistics from any arbitrary bivariate distribution function is established. This recurrence relation is the first bivariate version of the basic triangle rule for order statistics arisen from univariate distribution function. Finally, this relation is extended to the trivariate case. These lead to similar identities for product moments (of any order) of order statistics. 相似文献
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In this paper, we study the weak convergence of the random maximum of independent and non-identical random vectors. When the random sample size is assumed to be independent of the basic variables and its distribution function is assumed to converge weakly to a non-degenerate limit, the necessary and sufficient conditions for the weak convergence of the random maximum are derived. An illustrative example is given. 相似文献