Department of Mathematics and Statistics, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, India.
Department of Statistics, Tribhuvan University, Birendra Multiple Campus, Bharatpur, Nepal.
PLoS One. 2022 Jun 3;17(6):e0269450. doi: 10.1371/journal.pone.0269450. eCollection 2022.
This study suggested a new four-parameter Exponentiated Odd Lomax Exponential (EOLE) distribution by compounding an exponentiated odd function with Lomax distribution as a generator. The proposed model is unimodal and positively skewed whereas the hazard rate function is monotonically increasing and inverted bathtubs. Some important properties of the new distribution are derived such as quintile function and median; asymptotic properties and mode; moments; mean residual life, mean path time; mean deviation; order statistics; and Bonferroni & Lorenz curve. The value of the parameters is obtained from the maximum likelihood estimation, least-square estimation, and Cramér-Von-Mises methods. Here, a simulation study and two real data sets, "the number of deaths per day due to COVID-19 of the first wave in Nepal" and ''failure stresses (In Gpa) of single carbon fibers of lengths 50 mm", have been applied to validate the different theoretical findings. The finding of an order of COVID-19 deaths in 153 days in Nepal obey the proposed distribution, it has a significantly positive relationship between the predictive test positive rate and the predictive number of deaths per day. Therefore, the intended model is an alternative model for survival data and lifetime data analysis.
本研究提出了一种新的四参数指数奇数 Lomax 指数（EOLE）分布，方法是将指数奇数函数与 Lomax 分布复合作为生成器。所提出的模型是单峰的，偏态为正，而危险率函数是单调递增的，呈倒置的浴盆状。推导出了新分布的一些重要性质，如五分位数函数和中位数；渐近性质和模式；矩；平均剩余寿命、平均路径时间；平均偏差；顺序统计量；以及 Bonferroni 和 Lorenz 曲线。参数值是通过最大似然估计、最小二乘估计和 Cramér-Von-Mises 方法获得的。这里，进行了模拟研究和两个实际数据集，即“尼泊尔第一波 COVID-19 每日死亡人数”和“长度为 50mm 的单根碳纤维的失效应力（以 Gpa 为单位）”，以验证不同的理论发现。尼泊尔 COVID-19 死亡人数的顺序在 153 天内服从所提出的分布，预测阳性率和预测每日死亡人数之间存在显著的正相关关系。因此，所提出的模型是生存数据分析和寿命数据分析的替代模型。
