ABSTRACT

In the literature of distribution theory, a vast proportion is acquired by discrete distributions and their applications in real-world phenomena. However, in a rapidly changing technological era, the data generated is becoming increasingly complex day by day, making it difficult for us to capture various aspects of this real data through existing discrete models. In view of this, we propose a new flexible discrete distribution with one parameter. Some statistical and reliability are derived. These properties can be expressed as closed-forms. One of the important virtues of this newly evolved model is that it can model not only over-dispersed, positively skewed and leptokurtic data sets, but it can also be utilized for modeling increasing, decreasing and unimodal failure rate. Various estimation approaches are utilized to estimate the model parameter. A simulation study is carried out to examine the performance of the estimators for different sample size. The flexibility of the new model for analyzing different types of data is explained by utilizing four real data sets in different fields. Finally, the proposed model can serve as an alternative model to other distributions in the existing literature for modeling positive real data in several areas.

摘要

在分布理论的文献中，很大一部分是通过离散分布及其在现实世界现象中的应用获得的。然而，在瞬息万变的技术时代，产生的数据日益复杂，我们很难通过现有的离散模型来捕捉这些真实数据的各个方面。鉴于此，我们提出了一种新的具有一个参数的灵活离散分布。得出了一些统计和可靠性。这些属性可以表示为封闭形式。这种新发展的模型的重要优点之一是它不仅可以对过度分散、正偏斜和尖峰数据集进行建模，而且还可以用于对增​​加、减少和单峰故障率进行建模。使用各种估计方法来估计模型参数。进行了模拟研究以检查不同样本大小的估计器的性能。通过利用不同领域的四个真实数据集来解释分析不同类型数据的新模型的灵活性。最后，所提出的模型可以作为现有文献中其他分布的替代模型，用于对多个领域的正真实数据进行建模。