Posterior Distribution of the Unknown Parameter of Poisson Distribution Under Different Priors: An Application to Under-Fivemortality Data

Abstract

Under-five mortality rate is one of the most essential indicator of acountry’s socio-economic well-being and public health status. Poissondistribution under different priors such as conjugate/Gamma prior,uniform and Jeffrey’s prior is used to obtain posterior distribution ofthe unknown parameter with an application to under-five mortalitydata in six East Africa countries from 1960 to 2020. The estimatesare examined through a Bayesian analysis while all the calculationsare carried out the R-statistical software and MS Excel. Among allpriors used in this study, conjugate prior was found to be compatiblefor the unknown parameters of the Poisson distribution. The casesof under-five mortality are found to reduce over time. East Africacountries through East Africa Community (EAC) should build strongand resilient health systems, identify and prioritize interventions tomitigate under-five mortality among Member States.