In this paper, a new family of polyno-expo-trigonometric distributions is presented and investigated. A special case using the Weibull distribution, with three parameters, is considered as statistical model for lifetime data. The estimation of the parameters is performed with the maximum likelihood method. A numerical simulation study verifies that the bias and the mean squared error of the maximum likelihood estimators tend to zero as the sample size is increased. Three real life datasets are then analyzed. We show that our model has a good fit in comparison to the other well-known powerful models in the literature.

中文翻译：

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具有应用的新的多项式-指数-三角分布族

在本文中，提出并研究了一个新的多项式-指数-三角分布族。使用具有三个参数的 Weibull 分布的特殊情况被认为是寿命数据的统计模型。使用最大似然法进行参数的估计。数值模拟研究证实，随着样本量的增加，最大似然估计量的偏差和均方误差趋于零。然后分析三个现实生活数据集。我们表明，与文献中其他著名的强大模型相比，我们的模型具有很好的拟合度。