This paper proposes a new flexible discrete triplet Lindley model that is constructed from the balanced discretization principle of the extended Lindley distribution. This model has several appealing statistical properties in terms of providing exact and closed form moment expressions and handling all forms of dispersion. Due to these, this paper explores further the usage of the discrete triplet Lindley as an innovation distribution in the simple integer-valued autoregressive process (INAR(1)). This subsequently allows for the modeling of count time series observations. In this context, a novel INAR(1) process is developed under mixed Binomial and the Pegram thinning operators. The model parameters of the INAR(1) process are estimated using the conditional maximum likelihood and Yule-Walker approaches. Some Monte Carlo simulation experiments are executed to assess the consistency of the estimators under the two estimation approaches. Interestingly, the proposed INAR(1) process is applied to analyze the COVID-19 cases and death series of different countries where it yields reliable parameter estimates and suitable forecasts via the modified Sieve bootstrap technique. On the other side, the new INAR(1) with discrete triplet Lindley innovations competes comfortably with other established INAR(1)s in the literature.

中文翻译：

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平衡离散三元组 Lindley 模型及其 INAR(1) 扩展：属性和 COVID-19 应用

本文提出了一种新的灵活离散三元组 Lindley 模型，该模型是根据扩展 Lindley 分布的平衡离散化原理构造的。该模型在提供精确和封闭形式矩表达式以及处理所有形式的色散方面具有几个吸引人的统计特性。因此，本文进一步探讨了离散三元组 Lindley 作为简单整数值自回归过程 (INAR(1)) 中的创新分布的使用。这随后允许对计数时间序列观察进行建模。在此背景下，在混合二项式和 Pegram 细化算子下开发了一种新颖的 INAR(1) 过程。INAR(1) 过程的模型参数使用条件最大似然法和 Yule-Walker 方法进行估计。进行一些蒙特卡罗模拟实验来评估两种估计方法下估计量的一致性。有趣的是，拟议的 INAR(1) 流程用于分析不同国家的 COVID-19 病例和死亡系列，通过修改后的 Sieve bootstrap 技术产生可靠的参数估计和合适的预测。另一方面，具有离散三重态 Lindley 创新的新 INAR(1) 可以与文献中其他成熟的 INAR(1) 轻松竞争。