Partial Bayes Estimation in Two-Parameter Rayleigh Distribution

In Bayesian paradigm, when we have no proper information regarding the joint parameters of the model of the variable and the aim is to estimate only one of them in presence of another nuisance parameter, we introduce an estimation approach known as ‘Partial Bayes estimation’. Here, two-parameter Rayleigh distribution is considered with location parameter μ and scale parameter λ and both are unknown. Partial Bayes estimates of the parameter of interest λ are derived both under non-informative uniform prior and informative gamma prior by plugging the estimate of another parameter μ, obtained by some other classical method using ordered samples. As, the maximum likelihood estimate of the parameters cannot be obtained explicitly, we also propose an estimation method closed to maximum likelihood estimate using the ordered samples. We use Kullback-Leibler distance loss derived using two Rayleigh density functions, precautionary loss and weighted squared error loss functions to compute the risk values. Simulation studies are performed to assess the performance of the Partial Bayes estimates through integrated risks under different loss functions. Two real datasets are used to show the applicability of the proposed Partial Bayes estimation technique.