Birbiçer İsmet, Genç Ali I
Department of Statistics, Cukurova University, Adana, Turkey.
J Appl Stat. 2022 Jul 19;50(15):3108-3124. doi: 10.1080/02664763.2022.2101045. eCollection 2023.
The standard omega distribution is defined on the unit interval so that it is a probabilistic model for observations in rates and percentages. It is, in fact, the unit form of the exponentiated half logistic distribution. In this work, we first give a detailed shape analysis from which we observe that it is another flexible beta-like distribution. We observe that it can be J-shaped, reverse J-shaped, U-shaped, unimodal and show left and right skewness according to the values of its shape parameters. Contrary to the ordinary beta, it has the advantage of having a clear distribution function. We then discuss the existence and uniqueness of the maximum likelihood estimators and the Bayesian estimate of the parameters. The existence and uniqueness of the maximum likelihood estimators of the parameters will give a great advantage to the possible practitioners of this model since the possibility of finding a spurious solution to the likelihood equations disappears then. The comparison of these estimators with the existing ones for the general omega distribution is made with the help of a simulation study. Two real data fitting demonstrations prove its usefulness among other beta-like distributions such as Kumaraswamy, log-Lindley and Topp-Leone.
标准欧米伽分布定义在单位区间上，因此它是比率和百分比观测值的概率模型。事实上，它是指数化半逻辑分布的单位形式。在这项工作中，我们首先进行详细的形状分析，从中观察到它是另一种灵活的类似贝塔的分布。我们观察到它可以是J形、倒J形、U形、单峰的，并根据其形状参数的值呈现左偏和右偏。与普通贝塔分布不同，它具有分布函数清晰的优点。然后我们讨论最大似然估计量的存在性和唯一性以及参数的贝叶斯估计。参数最大似然估计量的存在性和唯一性将给该模型的潜在使用者带来很大优势，因为那时找到似然方程的虚假解的可能性就不存在了。借助模拟研究，将这些估计量与一般欧米伽分布的现有估计量进行了比较。两个实际数据拟合演示证明了它在其他类似贝塔的分布（如库马拉斯瓦米分布、对数林德利分布和托普 - 利昂分布）中的有用性。
