Department of Statistics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan.
PLoS One. 2021 Jan 14;16(1):e0245253. doi: 10.1371/journal.pone.0245253. eCollection 2021.
The main goal of the current paper is to contribute to the existing literature of probability distributions. In this paper, a new probability distribution is generated by using the Alpha Power Family of distributions with the aim to model the data with non-monotonic failure rates and provides a better fit. The proposed distribution is called Alpha Power Exponentiated Inverse Rayleigh or in short APEIR distribution. Various statistical properties have been investigated including they are the order statistics, moments, residual life function, mean waiting time, quantiles, entropy, and stress-strength parameter. To estimate the parameters of the proposed distribution, the maximum likelihood method is employed. It has been proved theoretically that the proposed distribution provides a better fit to the data with monotonic as well as non-monotonic hazard rate shapes. Moreover, two real data sets are used to evaluate the significance and flexibility of the proposed distribution as compared to other probability distributions.
本文的主要目标是为现有的概率分布文献做出贡献。本文通过使用幂函数族生成一个新的概率分布，旨在对具有非单调失效率的数据集进行建模，并提供更好的拟合。所提出的分布称为幂函数指数瑞利逆分布或简称 APEIR 分布。本文研究了各种统计性质，包括顺序统计量、矩、剩余寿命函数、平均等待时间、分位数、熵和应力-强度参数。为了估计所提出分布的参数，采用了最大似然法。从理论上证明，该分布对具有单调和非单调风险率形状的数据提供了更好的拟合。此外，使用两个真实数据集来评估与其他概率分布相比，所提出的分布的显著性和灵活性。
