Affiliations: [a] Department of Statistics, St. Anthony's College, Shillong, Meghalaya, India | [b] Department of Mathematics, Jones Hall, The College of William and Mary, Williamsburg, VA, USA | [c] Department of Statistics, Visva-Bharati University, Santiniketan, India
Corresponding author: Tanujit Dey, Department of Mathematics, Jones Hall, The College of William and Mary, Williamsburg, VA 23185, USA. Tel.: +1 757 221 4628; Fax: +1 757 221 7400; E-mail: [email protected].
Abstract: In this article we present Bayes estimators of Maxwell parameter and their associated risk based on conjugate prior, with respect to both symmetric loss function (squared error loss) and asymmetric loss function (precautionary loss). We also obtain the highest posterior density interval for the Maxwell parameter, as well as, the HPD prediction intervals for a future observation from this distribution. We present an illustrative example to show how the Maxwell distribution fits in a data (laser transmission data) set. Finally, we perform Monte Carlo simulations to compare the performances of the Bayes estimates under different conditions.
Keywords: Bayes estimator, Bayes risk, precautionary loss function, risk function