ON THE BAYESIAN ANALYSIS OF EXTENDED WEIBULL-GEOMETRIC DISTRIBUTION
DOI:
https://doi.org/10.13052/jrss2229-5666.12210Keywords:
Extended Weibull Distribution, Mcmc, Bayes Estimator, Posterior Risk, Loss Function, Precautionary Loss FunctionAbstract
The paper deals with the Bayes estimation of Extended Weibull-Geometric (EWG) distribution. In particular, we discuss Bayes estimators and their posterior risks using the noninformative and informative priors under different loss functions. Since the posterior summaries cannot be obtained analytically, we adopt Markov Chain Monte Carlo (MCMC) technique to assess the performance of Bayes estimates for different sample sizes. A real life example is also part of this study.
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References
Adamidis, K. and Loukas, S. (1998). A lifetime distribution with decreasing failure rate, Statistics & Probability Letters, 39, p. 35-42.
Ali, A., Sultan, Z. and Mutairi, A. (2017). The extended Weibull-Geometric distribution: properties and application, Journal of the North for Basic & Applied Sciences, 2, p. 108-125.
Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances, Philosophical Transactions of the Royal Society of London, 53, p. 370-418.
Banerjee, A. and Kundu, D. (2008). Inference based on Type-II Hybrid Censored Data from a Weibull distribution, IEEE Transaction Reliability, 57(2), p. 369-378.
Barreto-Souza, W., de Morais, A. L. and Cordeiro, G. M. (2011). The Weibull-geometric distribution, Journal of Statistical Computation and Simulation, 81 (5), p. 645-657.
Dey, S., Ali, S., and Park, C. (2015). Weighted exponential distribution: properties and different methods of estimation, Journal of Statistical Computation and Simulation, 85(18), p. 3641-3661.
Dey, S., Dey, S., Ali, S., and Mulekar, M. S. (2016). Two-parameter Maxwell distribution: Properties and different methods of estimation, Journal of Statistical Theory and Practice, 10 (2), p. 291-310.
Dey, S., Zhang, C., Asgharzadeh, A., and Ghorbannezhad, M. (2017). Comparisons of methods of estimation for the NH distribution, Annals of Data Science, 4(4), p. 441-455.
Frechet, M. (1927). Sur la loi de probabilit de l'ecart maximum, Soci'et'e Polonaise de Mathematique Annales, 6, p. 93-116.
Geisser, S. (1984). On prior distributions for binary trials, The American Statistician, 38(4), p. 244-247.
Geilks, W. R. and Wild, P. (1992). Adaptive Rejection Sampling for Gibbs Sampling, Applied Statistics, 41(2), p. 337-348.
Keller, A. Z., Goblin, M. T. and Farnworth, N. R. (1985). Reliability analysis of commercial vehicle engines, Reliability Engineering, 10(1), p. 15-25.
Kundu, D. and Gupta, R. D. (2006). Estimation of P [Y < X] for Weibull distributions, IEEE Transactions on Reliability, 55 (2), p. 270-280.
Kuş, C. (2007). A new lifetime distribution. Computational Statistics & Data Analysis, 51, p. 4497-4509.
Laplace, P. S. (1820). Theorie analytique des probabilities (Paris: Gautheir- Villars).
Mudholkar, G. S., Srivastava, D. K. and Freimer, M. (1995). The exponentiated Weibull family: a reanalysis of the bus-motor-failure data, Technometrics, 37(4), p. 436-445.
Mudholkar, G. S. and Huston, A. D. (1996). The exponentiated weibull family:some properties and a flood data application, Communications In Statistics-Theory and Methods, 25(12), p. 3059-3083.
Rinne, H. (2008). The Weibull Distribution: A Handbook, Champman and Hall/CRC Press
Rosin, P. and Rammler, E. (1933). The laws governing the fineness of powdered coa,. Journal of the Institute of Fuel, 7, p. 29-36.
Ramos, M. A., Moala, F. A. and Achcar, J. A. (2014), Bayesian estimation of Geometric distribution parameter under entropy Loss function, Application of Statistics and Management, 27(1), p. 82-86.
Stoyan, D. (2013), Weibull, RRSB, or extreme-value theorists, Metrika, 76, p. 153-159.
Saqib, M. and Dar, I. S. (2016). Bayesian analysis of the Weibull lifetimes under type-i ordinary right censored samples, Pakistan Journal of Statistics and Operational Research, XII (3), p. 533-545.
Singh, S. K., Singh, U. and Kumar, M. (2014). Estimation for the parameter of Poisson-exponential distribution under Bayesian paradigm, Journal of Data Science, 12, p. 157-173.
Sultana, T. and Aslam, M., (2017), bayesian estimation of 3-component mixture of the inverse Weibull distributions, Iranian Journal of Science and Technology, Transactions A:Science. 41(4), p. 1-9.
Sultana, T., Aslam, M. and Raftab, M., (2017). Bayesian estimation of 3- component mixture of Gumbel type-II distributions under non-informative and informative priors, Journal of National Science Foundation of Srilanka. 45(3), p. 287-306.
Wang, M. and Elbatal, I. (2015). The modified Weibull-Geometric distribution, Metron, 73 (3), p. 303-315.
Weibull, W. and Stockholm, S. (1951). A statistical distribution function of wide applicability, Journal of Applied Mechanics, Transition ASME, 73, p. 293-297.
Yousaf, F., Ali, S., and Shah, I. (2019), Statistical inference for the Chen distribution based on upper record values, https://doi.org/10.1007/s40745- 019-00214-7.