A new generalized class of distributions called the Lindley-Burr XII Power Series (LBXIIPS) distribution is proposed and explored. This new class of distributions contain some special cases such as Lindley-Burr XII Poisson (LBXIIP), Lindley-Burr XII Logarithmic (LBXIIL), Lindley-Burr XII Binomial (LBXIIB) and their sub-models among others. Some structural properties of the new distribution including moments, probability weighted moments, distribution of the order statistics and entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and finally, an application to a real data set in order to illustrate the usefulness of the new distribution is given.
展开▼
机译：提出并探索了一种新的广义分布，称为Lindley-Burr XII电源系列（LBXiIPS）分布。这类新的分布包括一些特殊案例，如Lindley-Burr Xii Poisson（LBXIIP），Lindley-Burr XII对数（LBXIIL），Lindley-Burr XII二项式（LBXIIB）及其子模型等。推导出包括矩，概率加权时刻的新分布的一些结构特性，得到了订单统计和熵的分布。最大似然估计技术用于估计模型参数。提出了一种仿真研究，以呈现最大似然估计器的偏差和均方误差，最后，给出了真实数据集的应用，以便说明新分布的有用性。
展开▼
