Density Estimation of Neonatal Mortality Rate Using Empirical Bayes Deconvolution in Central Java Province, Indonesia

This article is concerned with the density estimation of Neonatal Mortality Rate (NMR) in Central Java Province, Indonesia. Neonatal deaths contribute to 73% of infant deaths in Central Java Province. The number of neonatal deaths for 35 districts/municipalities in Central Java Province is considered as Poisson distributed surrogate with NMR as the rate of Poisson distribution. It is assumed that each number of neonatal deaths by district/municipality in Central Java Province were realizations of unobserved NMR, which come from unknown prior density. We applied the Empirical Bayes Deconvolution (EBD) method for estimating the unknown prior density of NMR based on Poisson distributed surrogate. We used secondary data from the Health Profiles of Central Java Province, Indonesia, in 2018. The density estimation of NMR by the EBD method showed that the resulting prior estimate is relatively close to the Gamma distribution based on Poisson surrogate. This is implying that the suitability of the obtained prior density estimation as a conjugate prior for Poisson distribution.