Bayesian estimation of the parameter of a generalized geometric series distribution under different prior distributions and loss functions

Article type: Research Article

Authors: Dey, Sanku^a | Dey, Tanujit^{b; *} | Leemis, Lawrence^b

Affiliations: [a] Department of Statistics, St. Anthony's College, Shillong, Meghalaya, India | [b] Department of Mathematics, The College of William & Mary, Williamsburg, VA, USA

Correspondence: [*] Corresponding author. Tel.: +1 757 221 4628; Fax: +1 757 221 7400; E-mail: [email protected].

Abstract: Comparisons of estimates between the Bayes and frequentist methods are fascinating and challenging theme of interest in statistics with significant impact on professionals. For Bayes estimators, the performance depends on the form of the prior distribution and the assumed loss function. This paper illustrates the problem of estimation of the one-parameter generalized geometric series distribution, using conjugate and improper prior distributions under symmetric and asymmetric loss functions. Performance of the Bayes estimates with respect to different priors, loss functions, and maximum likelihood estimates are illustrated for a data set and through a simulation study.

Keywords: Bayes estimator, generalized geometric series distribution, general entropy loss function, quadratic loss function, squared error loss function

DOI: 10.3233/MAS-2011-0182

Journal: Model Assisted Statistics and Applications, vol. 6, no. 2, pp. 111-119, 2011