Anyiam Kizito E, Alghamdi Fatimah M, Nwaigwe Chrysogonus C, Aljohani Hassan M, Obulezi Okechukwu J
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
Department of Mathematical Sciences, College of Science, Princess Nuorah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia.
Heliyon. 2024 Sep 26;10(19):e38293. doi: 10.1016/j.heliyon.2024.e38293. eCollection 2024 Oct 15.
In this study, the Topp-Leone family of distribution approach was used to modify the Burr Hatke Exponential distribution to provide adequate fits for some engineering and health data which previous existing distributions in the family of Burr Hatke Exponential have failed to do. The new distribution improves the robustness of Burr Hatke Exponential distribution by making it capable of modeling emerging new world complex data with varying features, possesses greater capacity and flexibility to model lifetime data, has better goodness of fit. Some mathematical properties of the derived distribution such as quantile function, moments, order statistics, entropies, etc were obtained and discussed. Some non-Bayesian estimation approaches like maximum likelihood estimation (ML), maximum Product spacing estimation (MPSE), Least squares estimation (LS), weighted least squares estimation (WLS), Cramer-von-Mises estimation (CVM), Anderson-Darling estimation (AD), and right-tailed Anderson Darling estimation (RTAD), as well as Bayesian method under independent gamma priors were adopted to estimate the parameters of the model and the various methods proved efficient. From the simulation results, the bias and root mean squared error for the parameters are relatively small and the become smaller as the sample size becomes larger. This shows convenience and improved estimation accuracy. We further constructed a regression model using the proposed distribution. Extensive simulation studies were used to determine the efficiency of the method in both the estimation of its parameters and that of the regression model. The TL-BHE regression was fitted on censored CD4 count data of HIV/AIDs patients. The competitiveness, applicability, and usefulness of the model were demonstrated using datasets and the results validate the theoretical findings. The results indicate that the TL-BHE distribution achieved better results than the baseline distribution and other variants of the classical distributions.
在本研究中，使用Topp-Leone分布族方法对Burr Hatke指数分布进行修正，以便为一些工程和健康数据提供充分拟合，而Burr Hatke指数分布族中先前存在的分布未能做到这一点。新分布通过使其能够对具有不同特征的新兴复杂数据进行建模，提高了Burr Hatke指数分布的稳健性，具有更大的能力和灵活性来对寿命数据进行建模，拟合优度更好。获得并讨论了导出分布的一些数学性质，如分位数函数、矩、顺序统计量、熵等。采用了一些非贝叶斯估计方法，如最大似然估计（ML）、最大乘积间距估计（MPSE）、最小二乘估计（LS）、加权最小二乘估计（WLS）、克拉默-冯米塞斯估计（CVM）、安德森-达林估计（AD）和右尾安德森-达林估计（RTAD），以及独立伽马先验下的贝叶斯方法来估计模型参数，各种方法都证明是有效的。从模拟结果来看，参数的偏差和均方根误差相对较小，并且随着样本量的增大而变小。这表明了其便利性和估计精度的提高。我们进一步使用所提出的分布构建了一个回归模型。通过广泛的模拟研究来确定该方法在参数估计和回归模型估计方面的效率。将TL-BHE回归应用于HIV/AIDS患者的截尾CD4计数数据。使用数据集证明了该模型的竞争力、适用性和实用性，结果验证了理论发现。结果表明，TL-BHE分布比基线分布和经典分布的其他变体取得了更好的结果。
