两参数逆威布尔分布顺序统计量的矩及渐近分布  

Moments and Asymptotic Distributions of Order Statistics from Inverse Weibull Distribution with Two Parameters

作　　者：姜培华 JIANG Peihua(School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China)

机构地区：[1]安徽工程大学数理学院,安徽芜湖241000

出　　处：《南通大学学报（自然科学版）》2018年第1期75-80,共6页Journal of Nantong University(Natural Science Edition)　

基　　金：国家自然科学基金项目(11226218);安徽省高等教育提升计划省级自然科学研究一般项目(TSKJ2015B29);安徽省自然科学基金项目(1208085QA04)

摘　　要：设{X_k,1≤k≤n}独立同分布,X_((1)),X_((2)),…,X_((n))为其顺序统计量,当总体服从参数为(m,η)的逆威布尔分布时,得到其顺序统计量的概率密度、高阶矩和方差的表达式.证明了样本间隔不独立且不同分布,当k(k>1))固定时,得到顺序统计量X_((n-k+1))和X_((n))的渐近分布,最后给出一个关于并联系统寿命的应用实例.Let {Xk, 1≤k≤n} be independent and identically distributed random variables, and X（1）, X（2）, …, X（n）be their order statistics. The probability density function of its order statistics and the moments precise calculation formula were obtained, when X（k）followed Inverse Weibull distribution with parameters（m, η）. It was proved that the sample intervals of their order statistics are neither independent nor identically distributed. For a fixed integer k 1, the asymptotic distributions of the extremer order statistic X（（n））and X（（n-k ＋ 1））were also obtained. Finally, application example about the life of parallel system was given.

关 键 词：逆威布尔分布 顺序统计量 矩 渐近分布 

分 类 号：O211.4[理学—概率论与数理统计]