Fundamental Properties of the Characteristic Function using the Compound Poisson Distribution as the Sum of the Gamma Model
Mohammed Amine Meraou, Noriah M. Al-Kandari, Raqab Z. Mohammad
Abstract
Probability distribution has proven its usefulness in almost every discipline of human endeavor. For this, the zero-truncated Poisson gamma (ZTP-G) model is widely recognized in probability theory and extensively used in various applied fields, specifically in survival, hydrology, insurance, and energy theory. The characterization of the zero-truncated Poisson sum of independent and identically distributed gamma random variables is proposed in this paper by applying the Laplace-Stieltjes transform technique. Further, the properties of continuity and quadratic form of the characteristic function are applied for definite positive properties from the ZTP-G model.
Topics & Concepts
Poisson distributionCompound Poisson distributionDistribution (mathematics)Gamma distributionMathematicsStatistical physicsFunction (biology)Zero-inflated modelCompound Poisson processApplied mathematicsStatisticsMathematical analysisPhysicsPoisson regressionPoisson processSociologyBiologyDemographyEvolutionary biologyPopulationEngineering Diagnostics and ReliabilityStatistical Distribution Estimation and Applications