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.%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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