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

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.