Tweedie-Poisson regression-based mean estimation of dose equivalence rates using gamma count auxiliary information

The present paper suggests a new family of mean estimators based on the Tweedie-Poisson regression coefficient in order to efficiently estimate the dose equivalence rates in the environment using auxiliary information from gamma radiation counts. The commonly used traditional mean estimators, especially those based on Poisson regression, do not perform well in overdispersion and structurally heterogeneous variance that frequently arise in radiation measurement data.To overcome this limitation, we propose a new family of ratio-type estimators of the mean, which is based on the Tweedie-Poisson regression coefficient, more general in the sense that the variance may be scaled as a power of the mean. Under simple random sampling, theoretical properties of estimators are established: bias and mean squared error (MSE). The empirical studies, which use actual radiation data and simulation analyses, prove that the proposed estimators are significantly better than the traditional estimators that are based on Poisson in terms of MSE and Percentage Relative Efficiency (PRE).