非对称Cauchy分布最大次序统计量的大数定律研究

On the Laws of Large Numbers for Maximum Order Statis⁃tics Based on Asymmetrical Cauchy Distribution

基于非对称Cauchy分布随机阵列构造最大次序统计量,研究其大数定律问题,其中非对称Cauchy分布期望不存在。利用随机变量截尾技术和控制收敛定理,获得最大次序统计量的弱大数律和强大数律,并指出所获弱大数律不能推广到强大数律。另外,给出产生非对称Cauchy分布算法,并开展最大次序统计量的弱大数律和强大数律数据模拟工作。

Based on asymmetrical Cauchy random variables whose expectations do not exist,we con-struct maximum order statistics and study the laws of large numbers for the maximum order statistics.By the truncation of random variables and dominated convergence theorem,we obtain the weak laws and strong laws of large numbers for maximum order statistics.It is pointed out that the weak laws can-not extend to the strong laws.Moreover,we give the algorithm of generation for the asymmetrical Cau-chy random variable,and do some simulations to illustrate the weak laws and strong laws of large num-bers for the maximum order statistics.