A Discrete Linear-Exponential Model: Synthesis and Analysis with Inference to Model Extreme Count Data

In this article, a novel probability discrete model is introduced for modeling overdispersed count data. Some relevant statistical and reliability properties including the probability mass function, hazard rate and its reversed function, moments, index of dispersion, mean active life, mean inactive life, and order statistics, are derived in-detail. These statistical properties are expressed in closed forms. The new model can be used to discuss right-skewed data with heavy tails. Moreover, its hazard rate function can be utilized to model the phenomena with a monotonically increasing failure rate shape. Different estimation approaches are listed to get the best estimator for modeling and reading the count data. A comprehensive comparison among techniques is performed in the case of simulated data. Finally, four real data sets are analyzed to prove the ability and notability of the new discrete model.