A new generalized asymmetric logistic distribution is defined. In some cases, existing three parameter distributions provide poor fit to heavy tailed data sets. The proposed new distribution consists of only three parameters and is shown to fit a much wider range of heavy left and right tailed data when compared with various existing distributions. The new generalized distribution has logistic, maximum and minimum Gumbel distributions as sub-models. Some properties of the new distribution including mode, skewness, kurtosis, hazard function, and moments are studied. We propose the method of maximum likelihood to estimate the parameters and assess the finite sample size performance of the method. A generalized logistic regression model, based on the new distribution, is presented. Logistic-log-logistic regression, Weibull-extreme value regression and log-Fréchet regression are special cases of the generalized logistic regression model. The model is applied to fit failure time of a new insulation technique and the survival of a heart transplant study.

中文翻译：

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广义逻辑分布及其回归模型

定义了一种新的广义不对称逻辑分布。在某些情况下，现有的三个参数分布无法很好地拟合重尾数据集。拟议的新分布仅包含三个参数，并且与各种现有分布相比，显示出适合更广泛的左右尾粗数据。新的广义分布具有逻辑，最大和最小Gumbel分布作为子模型。研究了新分布的一些属性，包括模式，偏度，峰度，危害函数和矩。我们提出了一种最大似然方法来估计参数并评估该方法的有限样本量性能。提出了基于新分布的广义逻辑回归模型。Logistic-log-logistic回归，Weibull极值回归和log-Fréchet回归是广义logistic回归模型的特例。该模型适用于拟合新绝缘技术的失效时间和心脏移植研究的生存期。