DOI: 10.12732/ijam.v37i2.5
BAYESIAN INFERENCE ON GOMPERTZ-LINDLEY
DISTRIBUTION BASED ON
DIFFERENT LOSS FUNCTIONS
R. A. Al-Jarallah 1,§ , M. E. Ghitany 1 , D. Kundu 2
1 Department of Statistics and Operations Research
Faculty
of Science, Kuwait University, KUWAIT
2 Department of Mathematics and Statistics
Indian Institute of Technology Kanpur, Pin 208016, INDIA
Abstract. In the present paper, we consider Bayesian estimation of the parameters and reliability function of the Gompertz Lindley distribution based on three different loss functions. Bayesian estimators are obtained by using different priors under the symmetric squared error and asymmetric linear exponential and general entropy loss functions. Approximate Bayes estimators are computed using Markov chain Monte Carlo (MCMC) methods. These estimators are compared by using bias and mean squared error through simulation study. Finally, a real life data application is reported as an illustration.
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DOI: 10.12732/ijam.v37i2.5
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 2
References
[1] F. Almathkour, A. Alothman, M.E. Ghitany, R.C. Gupta, J. Mazucheli, A Comparative study of various methods of estimation for Gompertz-Lindley distribution. International Journal of Applied Mathematics, 35, No 2 (2022), 347-364; DOI: 10.12732/ijam.v35i2.12.
[2] S. Brooks, Markov chain Monte Carlo method and its application. Journal of the Royal Statistical Society: Ser. D (The Statistician), 47, No 1 (1998), 69-100; DOI: 10.1111/1467-1884.00117.
[3] R. Calabria, G. Pulcini, Point estimation under asymmetric loss functions for left-truncated
Exponential samples. Communications in Statistics - Theory and Methods, 25 (1996), 585-600;
DOI: 10.1080/03610929608831715.
[4] M.N. Chang, P.V. Rao, Improved estimation of survival functions in the new-better-than-used class. Technometrics, 35, No 2 (1993), 192-203.
[5] S. Dey, Bayesian estimation of the shape parameter of the generalized exponential distribution under different loss functions. Pakistan Journal of Statistics and Operation Research, 6, No 2 (2010), 163-174.
[6] A. Gelman, J.B. Carlin, H.S. Stern, D.B. Rubin, Bayesian Data Analysis, Chapman and Hall/CRC (1995).
[7] S. Geman, D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, No 6 (1984), 721-741; DOI: 10.1109/tpami.1984.4767596.
[8] M. E. Ghitany, S. M. Aboukhamseen, A. A. Baqer, R. C. Gupta, Gompertz-Lindley distribution and associated inference. Communications in Statistics - Simulation and Computation, 51, No 5 (2022), 2599-2618; DOI: 10.1080/03610918.2019.1699113.
[9] W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 55, No 1 (1970), 97-109; DOI: 10.1093/biomet/57.1.97.
[10] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21, No 6 (1953), 1087-1092; DOI: 10.1063/1.1699114.
[11] R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria (2011); http://www.r-project.org/index.html.
[12] S.K. Singh, U. Singh, D. Kumar, Bayesian estimation of the exponentiated gamma parameters and reliability function under asymmetric loss functions. RAVSTAT - Statistical Journal, 9 (2011), 247-260.
[13] P.K. Singh, S.K. Singh, U. Singh, Bayes estimator of inverse Gaussian parameters under general entropy loss function using Lindley’s approximation. Communications in Statistics - Simulation and Computation, 37, No 9 (2008), 1750-1762; DOI: 10.1080/03610910701884054.
[14] A.F.M. Smith, G.O. Roberts, Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society: Ser. B (Methodological), 55, No 1 (1993), 3-23; DOI: 10.2307/2346063.
[15] H. Varian, A Bayesian approach to real estate assessment. In: Studies in Bayesian Econometrics and Statistics in Honor of Leonard J. Savage, Stephen E. Fienberg and A. Zellner, Eds. (1975), 195–208, North-Holland Publishing Company, Amsterdam, The Netherlands.
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