Alahmadi Amani Abdullah, Albalawi Olayan, Khashab Rana H, Johannssen Arne, Nasiru Suleman, Almarzouki Sanaa Mohammed, Elgarhy Mohammed
College of Science and Humanities, Shaqra University, Shaqra, Saudi Arabia.
Department of Statistics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia.
PLoS One. 2025 Jan 22;20(1):e0314237. doi: 10.1371/journal.pone.0314237. eCollection 2025.
The Weibull distribution is an important continuous distribution that is cardinal in reliability analysis and lifetime modeling. On the other hand, it has several limitations for practical applications, such as modeling lifetime scenarios with non-monotonic failure rates. However, accurate modeling of non-monotonic failure rates is essential for achieving more accurate predictions, better risk management, and informed decision-making in various domains where reliability and longevity are critical factors. For this reason, we introduce a new three parameter lifetime distribution-the Modified Kies Weibull distribution (MKWD)-that is able to model lifetime scenarios with non-monotonic failure rates. We analyze the statistical features of the MKWD, such as the quantile function, median, moments, mean, variance, skewness, kurtosis, coefficient of variation, index of dispersion, moment generating function, incomplete moments, conditional moments, Bonferroni, Lorenz, and Zenga curves, and order statistics. Various measures of uncertainty for the MKWD such as Rényi entropy, exponential entropy, Havrda and Charvat entropy, Arimoto entropy, Tsallis entropy, extropy, weighted extropy and residual extropy are computed. We discuss eight different parameter estimation methods and conduct a Monte Carlo simulation study to evaluate the performance of these different estimators. The simulation results show that the maximum likelihood method leads to the best results. The effectiveness of the newly suggested model is demonstrated through the examination of two different sets of real data. Regression analysis utilizing survival times data demonstrates that the MKWD model offers a superior match compared to other current distributions and regression models.
威布尔分布是一种重要的连续分布，在可靠性分析和寿命建模中至关重要。另一方面，它在实际应用中存在一些局限性，比如对具有非单调失效率的寿命场景进行建模。然而，准确建模非单调失效率对于在可靠性和寿命是关键因素的各个领域实现更准确的预测、更好的风险管理和明智的决策至关重要。出于这个原因，我们引入了一种新的三参数寿命分布——修正基斯威布尔分布（MKWD），它能够对具有非单调失效率的寿命场景进行建模。我们分析了MKWD的统计特征，如分位数函数、中位数、矩、均值、方差、偏度、峰度、变异系数、离散指数、矩生成函数、不完全矩、条件矩、邦费罗尼曲线、洛伦兹曲线和曾加曲线以及顺序统计量。计算了MKWD的各种不确定性度量，如雷尼熵、指数熵、哈弗达和查尔瓦特熵、有元熵、Tsallis熵、外熵、加权外熵和剩余外熵。我们讨论了八种不同的参数估计方法，并进行了蒙特卡罗模拟研究以评估这些不同估计器的性能。模拟结果表明最大似然法产生的结果最佳。通过对两组不同的实际数据进行检验，证明了新提出模型的有效性。利用生存时间数据进行的回归分析表明，与其他当前分布和回归模型相比，MKWD模型提供了更好的拟合。
