New methods of extending base distributions are always invoke to increase their adaptability in modeling real life data. Recently, SMP method was introduced but Weibull distribution is yet to be explored through this method. First, we provide updated review on SMP transformed distributions. We then proposed and developed another extended Weibull distribution through this technique named SMPtW. Importantly, twelve of its statistical properties - reliability measures, quantile function, moment, stress-strength, mean waiting time, moment generating function, characteristics function, renyi entropy, order statistics, mean residual life and mode, were derived and studied extensively. The hazard function has a decreasing, increasing and constant shapes. We found a relation between the quantile of SMPtW and that of SMP Pareto distribution despite their difference in density functions. We adopt the inverse transform approach in random number generation and through simulation we evaluate maximum likelihood estimates (MLE) performance of its parameters. The result showed that MLE is consistent all through. The performance of the distribution was then examined using health dataset compared with five similar distributions. The results showed that three parameters SMPtW performed best among the competing models.

翻译：扩展基础分布的新方法总是被提出，以增强其在现实生活数据建模中的适应性。最近，SMP方法被引入，但威布尔分布尚未通过该方法得到探索。首先，我们对SMP变换分布提供了更新的综述。随后，我们通过该技术提出并发展了另一种扩展威布尔分布，命名为SMPtW。重要的是，我们推导并深入研究了其十二项统计特性——可靠性度量、分位数函数、矩、应力-强度、平均等待时间、矩生成函数、特征函数、Renyi熵、顺序统计量、平均剩余寿命和众数。其风险函数具有递减、递增和恒定三种形态。我们发现，尽管密度函数不同，SMPtW的分位数与SMP帕累托分布的分位数之间存在关联。在随机数生成中，我们采用逆变换方法，并通过模拟评估了其参数的最大似然估计（MLE）性能。结果表明，MLE在整个过程中具有一致性。随后，使用健康数据集将该分布与五种类似分布进行比较，以检验其性能。结果显示，三参数SMPtW在竞争模型中表现最佳。