Indian Journal of Science and Technology
Year: 2016, Volume: 9, Issue: 16, Pages: 1-5
D. Sheeba Singh1*, M. Immaculate Mary1 and M. Muthu Kumar2
1Department of Mathematics, Noorul Islam University, Kumaracoil, Kanyakumari Dist - 629180, Tamil Nadu, India; [email protected], imam_aru[email protected] 2Department of Statistics, PSG College of Arts and Science, Coimbatore - 641014, Tamil Nadu, India; [email protected]
*Author of Corresponding: D. Sheeba Singh Department of Mathematics, Noorul Islam University, Kumaracoil, Kanyakumari Dist - 629180, Tamil Nadu, India; [email protected]
Objectives: Fuzzy Bayesian approach is implemented to enrich the probability updating process with fuzzy facts. Methods: In this paper, different methods of estimation are discussed for the parameters of Gompertz distribution when the available data are in the form of fuzzy numbers. Bayes estimators of the parameters are studied under different symmetric and asymmetric loss functions. The estimation procedures are discussed in details and compared via Monte Carlo simulations. Finally, a real data set which shows the TB affected people of the thirty districts of Tamil Nadu in the year 2009 to 2011 is investigated to explain the applicability of the proposed methods. Findings: Among all the loss functions which are provided here, Linear Exponential loss function is more preferable as compared to all other loss functions.
Keywords: Bayesian Estimation, Gompertz Distribution, Loss Functions, Simulation Mathematical Subject Classification: 628A6
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