Li Xingbei, Gong Qin, Chen Tingting
School of Management, Tianjin University of Commerce, Tianjin, 300134, China.
College of Science, Jiangxi University of Science and Technology, Ganzhou, 341000, China.
Sci Rep. 2025 Aug 7;15(1):28970. doi: 10.1038/s41598-025-13773-y.
This paper aims to construct a new transformed Weibull distribution model by mathematically transforming the Weibull distribution model. This model significantly enhances its applicability and flexibility by adjusting the shape and scale parameters of the random variables. We have detailed the analysis of the key statistical properties of the transformed Weibull distribution, including survival function, hazard function, quantile function, moment and moment-generating function, and order statistics, and have explored its heavy-tailed characteristics through mathematical proofs. We employed maximum likelihood estimation to estimate the model parameters and constructed asymptotic confidence intervals for the parameters. In addition, considering the application of Bayesian estimation under both information prior and non-information prior conditions, we used mixed Gibbs sampling to estimate the parameters under the Q-symmetric entropy loss function and the DeGroot loss function, and determined Bayesian credible intervals. To evaluate the performance of the estimation methods, we used Monte Carlo simulation to obtain the average parameter estimates under various estimation methods, and measured the accuracy of the estimation using mean square errors and mean biases. The applicability and effectiveness of the transformed Weibull distribution in practical data analysis have been confirmed by applying it to two real datasets.
本文旨在通过对威布尔分布模型进行数学变换来构建一个新的变换威布尔分布模型。该模型通过调整随机变量的形状和尺度参数，显著提高了其适用性和灵活性。我们详细分析了变换威布尔分布的关键统计特性，包括生存函数、风险函数、分位数函数、矩和矩生成函数以及顺序统计量，并通过数学证明探索了其重尾特性。我们采用最大似然估计来估计模型参数，并为参数构建了渐近置信区间。此外，考虑到在信息先验和非信息先验条件下的贝叶斯估计应用，我们使用混合吉布斯抽样在Q对称熵损失函数和德格鲁特损失函数下估计参数，并确定贝叶斯可信区间。为了评估估计方法的性能，我们使用蒙特卡罗模拟获得各种估计方法下的平均参数估计值，并使用均方误差和平均偏差来衡量估计的准确性。通过将变换威布尔分布应用于两个实际数据集，证实了其在实际数据分析中的适用性和有效性。
