In this article we are interested in a general class of distributions for independent not necessarily identically distributed random variables, closed under minima, that includes a number of discrete and continuous distributions like the Geometric, Exponential, Weibull or Pareto. The main parameter involved in this class of distributions is assumed to be time varying with several possible modeling options. This is of particular interest in reliability and survival analysis for describing the time to event or failure. The maximum likelihood estimation of the parameters is addressed and the asymptotic properties of the estimators are discussed. We provide real and simulated examples and we explore the accuracy of the estimating procedure as well as the performance of classical model selection criteria in choosing the correct model among a number of competing models for the time-varying parameters of interest.

中文翻译：

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具有时变参数的一般类分布的统计推断

在本文中，我们感兴趣的是独立的不一定同分布的随机变量的一般分布，在最小值下闭合，其中包括许多离散和连续分布，如几何、指数、威布尔或帕累托。假设此类分布中涉及的主要参数是随时间变化的，并具有几种可能的建模选项。这对描述事件或故障时间的可靠性和生存分析特别感兴趣。讨论了参数的最大似然估计，并讨论了估计量的渐近特性。