Abstract

This study proposes two new methods of goodness-of-fit (GOF) tests for progressively Type-II censored data from any continuous distribution. For the first method, we transform the original censored sample into an approximately independent and identically distributed normality complete sample, and perform a complete sample GOF test for normality thereafter based on the empirical cumulative distribution function (ECDF). This method merely requires one table of critical values for all the distributions. For the second method, we propose a parametric bootstrap GOF test based on test statistics proposed by Pakyari and Balakrishnan. This method does not require data transformation, but directly uses the observed censored sample to the GOF test. This proposed approach does not require some tables for critical values, which are constructed using parametric bootstrap samples. We estimate the power of the two proposed methods for several well-known parameter distributions, and compare the power of parametric bootstrap method with that of Pakyari and Balakrishnan through various censoring schemes. Simulation results reveal that two new methods both possess good power properties in detecting departure from the null distribution, and the parametric bootstrap method provides as good or better power than the method of Pakyari and Balakrishnan. Lastly, the proposed methods are applied to two real data sets from engineering reliability aspect to prove their practical versatility.

摘要

这项研究提出了两种新的拟合优度（GOF）测试方法，用于对来自任何连续分布的渐进式II型审查数据进行检验。对于第一种方法，我们将原始检查样本转换为近似独立且分布均匀的正态性完整样本，然后基于经验累积分布函数（ECDF）对正态性执行完整的样本GOF检验。此方法只需要一张表的所有分布的临界值。对于第二种方法，我们基于Pakyari和Balakrishnan提出的测试统计数据，提出了一个参数自举GOF测试。此方法不需要数据转换，而是直接将观察到的审查样本用于GOF测试。此提议的方法不需要一些关键值表，使用参数引导程序样本构建。我们估计了两种提出的方​​法对几种众所周知的参数分布的功效，并通过各种检查方案将参数自举方法与Pakyari和Balakrishnan的功效进行了比较。仿真结果表明，两种新方法均具有良好的幂特性，可以检测出零分布，并且自举方法比Pakyari和Balakrishnan方法具有更好或更好的功效。最后，从工程可靠性的角度将所提出的方法应用于两个真实的数据集，以证明其实用性。并通过各种审查方案将参数自举方法的功能与Pakyari和Balakrishnan的功能进行了比较。仿真结果表明，两种新方法均具有良好的幂特性，可以检测出零分布，并且自举方法比Pakyari和Balakrishnan方法具有更好或更好的功效。最后，从工程可靠性的角度出发，将所提出的方法应用于两个真实数据集，以证明其实用性。并通过各种审查方案将参数自举方法的功能与Pakyari和Balakrishnan的功能进行了比较。仿真结果表明，两种新方法均具有良好的幂特性，可以检测出零分布，并且自举方法比Pakyari和Balakrishnan方法具有更好或更好的功效。最后，从工程可靠性的角度出发，将所提出的方法应用于两个真实数据集，以证明其实用性。