| 关于Weibull分布顺序统计量的分布性质 |
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| 引用本文： | 姜培华. 关于Weibull分布顺序统计量的分布性质[J]. 安庆师范学院学报(自然科学版), 2012, 18(1): 47-50 |
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| 作者姓名： | 姜培华 |
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| 作者单位： | 安徽工程大学数理学院,安徽芜湖,241000 |
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| 基金项目： | 安徽工程科技学院青年基金项目(2007YQ018)资助 |
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| 摘 要： | 设{Xk,1≤k≤n}独立同分布,X(1)≤X(2)≤…≤X(n)为其顺序统计量,当X(k)服从参数为m和η的韦布尔分布时,得到了其顺序统计量的联合概率密度函数和极端顺序统计量的密度函数,进一步得到X(1)和X(n)数学期望与方差的表达式。此外还证明了当参数m≠1时,X(1),X(2)-X(1),…,X(n)-X(n-1)不独立且不同分布;当参数m=1时,X(1),X(2)-X(1),…,X(n)-X(n-1)独立但不同分布。
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| 关 键 词： | 顺序统计量 韦布尔分布 数学期望 方差 |
Distributional Properties of Order Statistics of Weibull Distribution |
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| JIANG Pei-hua. Distributional Properties of Order Statistics of Weibull Distribution[J]. Journal of Anqing Teachers College(Natural Science Edition), 2012, 18(1): 47-50 |
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| Authors: | JIANG Pei-hua |
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| Affiliation: | JIANG Pei-hua(School of Mathematics and physics,Anhui Polytechnic University,Wuhu,Anhui 241000,China) |
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| Abstract: | Let {Xk,1≤k≤n} be independent and identically distributed random variables,X(1)≤X(2)≤…≤X(n) be their order statistics.The joint probability density function of its order statistics and the density functions of extreme order statistics are derived,when X(k) followed Weibull distribution with parameter m and η.The mathematical expectations and variances of X(1) and X(n) are also obtained.What’s more it proved the sample intervals X(1),X(2)-X(1),…,X(n)-X(n-1) are not independent and not identical distributions when the parameter m≠1,the sample intervals X(1),X(2)-X(1),…,X(n)-X(n-1) are independent but not identical distributions when the parameter m=1. |
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| Keywords: | order statistic Weibull distribution mathematical expectation variance |
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