We introduce and study general mathematical properties of a new generator of continuous distributions with three extra parameters called the odd log-logistic logarithmic generated family of distributions. We present some special models and investigate the asymptotes and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Shannon and Rényi entropies and order statistics, which hold for any baseline model, are determined. We discuss the estimation of the model parameters by maximum likelihood. Further, we introduce the new family in long-term survival models. We illustrate the potentiality of the proposed models by means of four applications to real data.

中文翻译：

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奇对数逻辑对数生成的分布族，并在不同领域中有应用

我们介绍和研究具有三个额外参数（称为奇对数对数对数生成的分布族）的新型连续分布生成器的一般数学性质。我们提出一些特殊模型并研究渐近线和形状。新的密度函数可以表示为基于相同基线分布的指数密度的线性组合。确定了普通和不完整矩，分位数和生成函数，Shannon和Rényi熵以及阶数统计量（适用于任何基准模型）的显式表达式。我们讨论通过最大似然估计模型参数。此外，我们在长期生存模型中引入了新家族。我们通过对实际数据的四个应用来说明所提出模型的潜力。