This paper deals with the Bayesian estimation of the concentration parameter of the l-mode Von Mises distribution under the assumption of four types of loss functions and a non-conjugate prior density for the unknown parameter. On the part of loss functions, the Squared Error Loss Function (SELF), DeGroot Loss Function (DLF), Minimum Expected Loss (MELO) Function and Exponentially Weighted Minimum Expected Loss (EWMELO) Function have been considered. Bayes Risks of Bayes estimators corresponding to four loss functions have also been obtained.

Keywords : L-Mode Von Mises Distribution, Bayes Estimator, Squared Error Loss Function (SELF), Degroot Loss Function (DLF), Minimum Expected Loss (MELO) Function And Exponentially Weighted Minimum Expected Loss (EWMELO) Function. Bayes Risk