GAMLSS Regression Model Based on the Assumption of Poisson Inverse Gamma Distribution
Count data is a very important data type,which appears in many fields such as medicine,soci-ology,psychology,insurance,transportation and so on.However,the count data is often over-dispersion,which makes the ordinary Poisson regression model unexplained.In this paper,we introduce a type of mixed Poisson distributions to fit over-dispersed count data.Based on the existing Poisson generalized inverse Gaussian(PGIG)distribution,the Poisson-reciprocal inverse Gaussian(PRIG)distribution and the Poisson-inverse Gamma(PIGA)distribution,we use the flexibility of the GAMLSS(generalized ad-ditive models for location,scale and shape)model and construct a GAMLSS model under the assumption that the response variables follow PIGA distribution.In order to verify the performance of our model,the GAMLSS models under PIGA,PRIG,and NB distribution assumptions are applied to the vehicle insurance claim frequency data,and the models are evaluated according to global deviation,AIC and BIC.The results show that our model can fit the over-dispersed vehicle insurance claim frequency data better than the GAMLSS models under the assumptions of PRIG and NB distributions,and is an effec-tive model for dealing with over-dispersed count data.
mixed Poisson distributionover-dispersedPoisson-inverse Gamma distributionGAMLSS modelvehicle insurance claim frequency data
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