A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models
Emrah Altun
Abstract
Abstract This study introduces the Poisson-Bilal distribution and its associated two models for modeling the over-dispersed count data sets. The Poisson-Bilal distribution has tractable properties and explicit forms for its statistical properties. A new over-dispersed count regression model and integer-valued autoregressive process with flexible innovation distribution are defined and studied comprehensively. Two real data sets are analyzed to prove empirically the importance of proposed models. Empirical findings show that the Poisson-Bilal distribution has important application fields in time series and regression modeling.
Topics & Concepts
Autoregressive modelMathematicsPoisson regressionPoisson distributionCount dataSTAR modelDistribution (mathematics)Integer (computer science)Regression analysisApplied mathematicsStatisticsSeries (stratigraphy)EconometricsTime seriesComputer scienceMathematical analysisAutoregressive integrated moving averagePopulationDemographyPaleontologyProgramming languageBiologySociologyStatistical Distribution Estimation and ApplicationsStatistical Methods and Bayesian InferenceBayesian Methods and Mixture Models