Goual Hafida, Yousof Haitham M
Laboratory of Probability and Statistics, University of Badji Mokhtar, Annaba, Algeria.
Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt.
J Appl Stat. 2019 Jul 9;47(3):393-423. doi: 10.1080/02664763.2019.1639642. eCollection 2020.
In this work, we propose a new three parameter distribution called the Burr XII inverse Rayleigh model, this model is a generalization of the inverse Rayleigh distribution using the Burr XII family introduced by Cordeiro [. J. Stat. Comput. Simul. 88 (2018), pp. 432-456]. After studying the statistical characterization of this model, we construct a modified chi-squared goodness-of-fit test based on the Nikulin-Rao-Robson statistic in the presence of two cases: censored and complete data. We describe the theory and the mechanism of the statistic test which can be used in survival and reliability data analysis. We use the maximum likelihood estimators based on initial non grouped data. Then, we conduct numerical simulations to reinforce the results. For showing the applicability of our model in various fields, we illustrate it and the proposed test by applications to two real data sets for complete data case and two other data sets in the presence of right censored.
在这项工作中，我们提出了一种新的三参数分布，称为 Burr XII 逆瑞利模型，该模型是使用 Cordeiro [《统计计算与模拟杂志》88 (2018)，第 432 - 456 页] 引入的 Burr XII 族对逆瑞利分布的推广。在研究了该模型的统计特征后，我们在两种情况下（删失数据和完整数据）基于 Nikulin - Rao - Robson 统计量构建了一种修正的卡方拟合优度检验。我们描述了可用于生存和可靠性数据分析的统计检验的理论和机制。我们使用基于初始未分组数据的最大似然估计量。然后，我们进行数值模拟以强化结果。为了展示我们模型在各个领域的适用性，我们通过将其应用于完整数据情况的两个真实数据集以及存在右删失的另外两个数据集来说明该模型和所提出的检验。
