We propose and study a new compounded model to extend the half-Cauchy and power-Cauchy distributions, which offers more flexibility in modeling lifetime data. The proposed model is analytically tractable and can be used effectively to analyze censored and uncensored data sets. Its density function can have various shapes such as reversed-J and right-skewed. It can accommodate different hazard shapes such as decreasing, upside-down bathtub and decreasing-increasing-decreasing. Some mathematical properties of the new distribution can be determined from a linear combination for its density function such as ordinary and incomplete moments. The performance of the maximum likelihood method to estimate the model parameters is investigated by a simulation study. Further, we introduce the new log-power-Cauchy negative-binomial regression model for censored data, which includes as sub-models some widely known regression models that can be applied to censored data. Four real life data sets, of which one is censored, have been analyzed and the new models provide adequate fits.

中文翻译：

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幂-Cauchy负二项式：性质和回归

我们提出并研究了一种新的复合模型，以扩展半Cauchy和幂Cauchy分布，这为建模寿命数据提供了更大的灵活性。所提出的模型在分析上易于处理，可以有效地用于分析经过审查和未经审查的数据集。它的密度函数可以具有各种形状，例如反向J和右斜。它可以适应不同的危险形状，例如减小，倒置的浴缸和减小-增大-减小。新分布的一些数学性质可以通过其密度函数的线性组合来确定，例如正常矩和不完全矩。通过仿真研究研究了最大似然法估计模型参数的性能。进一步，我们介绍了用于审查数据的新的log-power-Cauchy负二项式回归模型，该模型包括一些可以应用于审查数据的众所周知的回归模型作为子模型。已经分析了四个现实生活数据集，其中一个被审查，新模型提供了足够的拟合度。