Bayesian Estimation of the Odd Lindley Exponentiated Exponential Distribution : Applications in-Reliability
Abstract
In this work, we investigate the estimation of the unknown parameters and the reliability characteristics ofthe Odd Lindley Exponentiated Exponential distribution. The Bayes estimators and corresponding risks are derived usingvarious loss functions with complete data and a gamma prior distribution. A simulation study was carried out to calculate allthe results. We used Pitman’s closeness criterion and the integrated mean squared error to compare the performance of theBayesian and maximum likelihood estimators. Finally, we illustrate our techniques by analysing a real-life data set.References
A. Chadli, H. Talhi, H. Fellag, Comparison of the maximum likelihood and bayes estimators for symmetric bivariate exponential distribution under different loss functions, Afr. Stat. vol 8, 499–514,2013.
A.Chadli, Khawla.B , Asma.M, and Fellag. H, Bayesian estimation of the rayleigh distribution under different loss function. Electronic Journal of Applied Statistical Analysis, vol 10, 50–64,2017.
A.Gross and Clark.V, Survival distributions: reliability applications in the biomedical sciences, John Wiley & Sons,1975.
B.Oluyede , Y. T, A new class of generalized Lindley distributions with applications, J.Stat. Comput.Simul. vol 85,2072–2100,2015.
C.Robert, The Metropolis Hastings algorithm, stat.CO. vol 1, 4757–4145,2015.
Elbatal, Ibrahim, Laba Handique, and Subrata Chakraborty. Truncated Cauchy Power Kumaraswamy Generalized Family of Distributions: Theory and Applications, Statistics, Optimization & Information Computing,2023.
E.Pitman,J, The closest estimates of statistical parameters, In Mathematical Proceedings of the Cambridge Philosophical Society. vol 33,212–222,1937.
F.Gomes-Silva, Ana Percontini, Edleide de Brito, Manoel W. Ramos, Ronaldo Venˆancio, Gauss Cordeiro, The Odd Lindley-G Family of Distributions, Austrian Journal of Statistics.vol 46, 65–87,2017 .
G.Chen and Balakrishnan, N, A general-purpose approximate goodness-of-fit test, Journal of Quality Technology.vol 27, 154–161,1995.
G.Hafida, Haitham M. Y, M. Masoom.A, Validation of the Odd Lindley Exponentiated Exponential by a Modified Goodness of Fit test and its Applications to Censored and Complete Data, Pak.j.stat.oper.res. vol 15,745-771,2019.
Handique, L., Aidi, K., Chakraborty, S., Elbatal, I., & Ali, M. M. Analysis and Model Validation of Right Censored Survival Data with Complementary Geometric-Topp-Leone-G Family of Distributions., International Journal of Statistical Sciences, 13-26, 2023.
H.Talhi and Aiachi. H, On truncated zeghdoudi distribution: Posterior analysis under different loss functions for type ii censored data, Pak.j.stat.oper.res. vol 17,497–508,2021.
J. Achcar, and Leonardo R.A, Use of Markov Chain Monte Carlo methods in a Bayesian analysis of the Block and Basu bivariate exponential, Annals of the Institute of Statistical Mathematics. vol50, 403–416,1998.
M.Ghitany, A. B, Nadarajah, Lindley distribution and its applications, Math.Comput.Simul. vol 8, 493–506,2008.
M.Jozani , Davies.K.F, B. N, Pitman closeness results concerning ranked set sampling, Statistics and Probability Letters. vol 82 2260–2269,2012.
M.Korkmaz, C. and Yousof, H. M, The one-parameter odd Lindley exponential model: mathematical properties and applications, Stochastics and Quality Control,vol 32,25–35,2017.
R.Levine, and Casella. G, Implementation of the Monte-Carlo EM algorithm, J.Comput. Graph. Statist, vol 10, 422–439,2001.
R.Gupta.D and Kundu.D, Exponentiated exponential family: analternative to gamma and Weibull distributions, Biom. J. vol 43, 117-–130,2001.
V.Ravi, G. P, BB: An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function, J. Statist. Software. vol 32,1–26,2009.
Y.Yang, Can the strengths of AIC and BIC be shared, A conict between model indentication and regression estimation. vol 92,937–950,2005.
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