RESUMEN
In this paper we proposed three estimators namely linear shrinkage, preliminary test and shrinkage preliminary test for the rate parameter of univariate gamma. The salient feature of the proposed estimators is the admissibility property that is defined on belief of the uncertain prior information. Expressions for bias and relative efficiency under method of moment have been derived using asymptotic theory. A Monte Carlo simulation study shows that the proposed estimators are more efficient and minimally biased when prior information is close to the neighbourhood of the rate parameter.
RESUMEN
The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.