The Binomial-Discrete Poisson-Lindley Model: Modeling and Applications to Count Regression (Communications in Mathematical Research, 2021)
On the basis of a well-established binomial structure and the so-called Poisson-Lindley distribution, a new two-parameter discrete distributionis introduced. Its properties are studied from both the theoretical and practical sides. For the theory, we discuss the moments, survival and hazard ratefunctions, mode and quantile function. The statistical inference on the modelparameters is investigated by the maximum likelihood, moments, proportions,least square, and weighted least square estimations. A simulation study is conducted to observe the performance of the bias and mean square error of theobtained estimates. Then, applications to two practical data sets are given.Finally, we construct a new flexible count data regression model called thebinomial-Poisson Lindley regression model with two practical examples in themedical area.
Keywords: Binomial-discrete family; Poisson-Lindley distribution; estimation; data analysis; count regression.