In this paper, we first study a new two parameter lifetime distribution. This distribution includes “monotone” and “non-monotone” hazard rate functions which are useful in lifetime data analysis and reliability. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Renyi entropy, δ-entropy, order statistics and probability weighted moments are derived. Non-Bayesian estimation methods such as the maximum likelihood, Cramer-Von-Mises, percentile estimation, and L-moments are used for estimating the model parameters. The importance and flexibility of the new distribution are illustrated by means of two applications to real data sets. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for the right censored validation, we then propose and apply a modified chi-square goodness-of-fit test for the Burr X Weibull model. The modified goodness-of-fit statistics test is applied for the right censored real data set. Based on the censored maximum likelihood estimators on initial data, the modified goodness-of-fit test recovers the loss in information while the grouped data follows the chi-square distribution. The elements of the modified criteria tests are derived. A real data application is for validation under the uncensored scheme.

中文翻译：

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一种新的参数寿命分布，带有改进的 Bagdonavičius-Nikulin 拟合优度检验，用于审查验证、属性、应用和不同的估计方法

在本文中，我们首先研究了一种新的双参数寿命分布。该分布包括“单调”和“非单调”危险率函数，它们在生命周期数据分析和可靠性方面很有用。推导出了它的一些数学性质，包括普通矩和不完全矩的显式表达式、生成函数、人一熵、δ-熵、阶统计量和概率加权矩。非贝叶斯估计方法如最大似然、Cramer-Von-Mises、百分位估计和L-矩用于估计模型参数。新分布的重要性和灵活性通过对实际数据集的两个应用来说明。使用 Bagdonavicius-Nikulin 拟合优度检验的方法进行正确的删失验证，然后，我们为 Burr X Weibull 模型提出并应用了修改后的卡方拟合优度检验。修正的拟合优度统计检验适用于右删失的真实数据集。基于初始数据的删失最大似然估计量，修正的拟合优度检验恢复了信息损失，而分组数据遵循卡方分布。导出修改后的标准测试的元素。一个真实的数据应用程序用于在未经审查的方案下进行验证。修改后的拟合优度检验恢复了信息损失，而分组数据遵循卡方分布。导出修改后的标准测试的元素。一个真实的数据应用程序用于在未经审查的方案下进行验证。修改后的拟合优度检验恢复了信息损失，而分组数据遵循卡方分布。导出修改后的标准测试的元素。一个真实的数据应用程序用于在未经审查的方案下进行验证。