Department of Mathematics, Umm Al-Qura University, Al-Qunfudah University College, Mecca, Saudi Arabia.
Department of Statistics, Faculty of Business Administration, Delta University of Science and Technology, Mansoura, Egypt.
Comput Intell Neurosci. 2021 Aug 29;2021:2167670. doi: 10.1155/2021/2167670. eCollection 2021.
In reliability studies, the best fitting of lifetime models leads to accurate estimates and predictions, especially when these models have nonmonotone hazard functions. For this purpose, the new Exponential-X Fréchet (NEXF) distribution that belongs to the new exponential-X (NEX) family of distributions is proposed to be a superior fitting model for some reliability models with nonmonotone hazard functions and beat the competitive distribution such as the exponential distribution and Frechet distribution with two and three parameters. So, we concentrated our effort to introduce a new novel model. Throughout this research, we have studied the properties of its statistical measures of the NEXF distribution. The process of parameter estimation has been studied under a complete sample and Type-I censoring scheme. The numerical simulation is detailed to asses the proposed techniques of estimation. Finally, a Type-I censoring real-life application on leukaemia patient's survival with a new treatment has been studied to illustrate the estimation methods, which are well fitted by the NEXF distribution among all its competitors. We used for the fitting test the novel modified Kolmogorov-Smirnov (KS) algorithm for fitting Type-I censored data.
在可靠性研究中，通过最佳拟合寿命模型可以得到准确的估计和预测，特别是当这些模型具有非单调风险函数时。为此，我们提出了一种新的指数-X Fréchet（NEXF）分布，它属于新的指数-X（NEX）分布家族，是一些具有非单调风险函数的可靠性模型的优越拟合模型，并击败了竞争分布，如二参数和三参数的指数分布和 Fréchet 分布。因此，我们专注于引入一种新的模型。在整个研究过程中，我们研究了 NEXF 分布的统计量的性质。在完整样本和 I 型删失方案下研究了参数估计过程。详细的数值模拟评估了所提出的估计技术。最后，研究了一种新的治疗白血病患者生存的 I 型删失的实际应用，以说明在所有竞争对手中，NEXF 分布都能很好地拟合。我们使用新的修正的 Kolmogorov-Smirnov（KS）算法来拟合 I 型删失数据，用于拟合检验。
