Shrinkage estimation of θα in gamma density G(1/θ, p) using prior information

Shrinkage estimation in the gamma density using prior information is valuable in various fields, including finance, healthcare, and environmental science, where accurate parameter estimation is essential for decision-making and modeling. This manuscript considers the problem of estimation of \(\theta^{\alpha }\) in Gamma density G(1/θ, p) when the prior estimate or guessed value of the parameter \(\theta^{\alpha }\) is available in the form of point estimate \(\theta_{0}^{\alpha }\). Some families of estimators of \(\theta^{\alpha }\) are defined with its properties. Estimators developed by other authors are identified as particular members of the suggested families of shrinkage estimators. In particular, we have discussed the properties of the suggested families of estimators in an exponential distribution with known coefficient of variation. Numerical illustrations are also given in order to judge the merits of the proposed families of estimators over others.