Abstract

The common used goodeness-of-fit tests are based on the empirical distributions functions (EDF) where distances between empirical and theoretical hypothesized distributions are compared to critical values. The aim of this paper is to provide for different sample sizes, tables of goodness-of-fit critical values of modified Kolmogorov-Smirnov statistic Dn,$D_n,$$D_n,$ Anderson-Darling statistic A², Cramer-Von Mises statistic W2,$W^2,$$W^2,$ Liao and Shimokawa statistic L_n, and Watson statistic U² for the competing risks model of Bertholon which is used to describe the reliability of real systems where failure times can have different risks and in medical studies to characterize the survival time of patients who can have risks of death from different causes. The power of these statistics is studied using some alternatives such as the exponential, the inverse Weibull, the exponentiated Weibull and the exponentiated exponential distributions. All the computation are carried out by using matlab software and Monte Carlo method.

摘要

常用的拟合优度检验基于经验分布函数 ( EDF )，其中将经验和理论假设分布之间的距离与临界值进行比较。本文的目的是提供不同样本量的修正 Kolmogorov-Smirnov 统计量的拟合优度临界值表Dn,$D_n,$$D_n,$Anderson-Darling 统计量A ²、Cramer-Von Mises 统计量瓦2,${瓦}^2,$$W^2,$Bertholon 竞争风险模型的Liao 和 Shimokawa 统计量L _n以及 Watson 统计量U ²用于描述真实系统的可靠性，其中故障时间可能具有不同的风险，并在医学研究中描述患者的生存时间不同原因导致的死亡风险。使用指数分布、逆威布尔分布、指数威布尔分布和指数指数分布等替代方法来研究这些统计量的功效。所有计算均采用matlab软件和蒙特卡罗方法进行。