Comparison of Maximum Likelihood and Approximate Bayes Estimators for unknown Parameters of Exponentiated Weibull Distribution

Şeyma Kubilay, buğra saraçoğlu


In this study ,it is considered comparison of approximate Bayes estimators and maximum likelihood estimators (MLEs) for the unknown parameters of  Exponentiated Weibull (EW) distribution. The Bayes estimators and MLEs can not be obtained in closed forms. But MLEs is computed Newton Raphson method and approximate bayes estimators are obtained by using Tierney-Kadane and Lindley methods. Moreover, the approximate Bayes estimators are compared with the MLEs in terms of mean risk by using Monte Carlo simulation method.


Bayes estimator, Exponentiated Weibull distribution, Lindley’s approximation, Maximum likelihood estimation, Monte Carlo simulation, Tierney-Kadane’s approximation.


Danish,M.Y. and Aslam,M., (2013). Bayesian Analysis of Randomly Censored Generalized Exponential Distribution. Austrıan Journal Of Statıstıcs Volume 42, Number 1, 47–62.

Dellaportas, P., Wright, D.E. (1991). Numerical prediction for the two-parameter Weibull distribution. The Statistician , 365-372.

Elshahat, M.A.T. (2008). Approximate Bayes estimators for the exponentiated Weibull parameters with progressive interval censoring, The 20th Annual Conference on Statistics & Modeling In Human & Social Science, Faculty of Economic & Political Science, Cairo University, Egypt, 123-136.

Gupta, R.D., Kundu, D. (2001), Exponentiated exponential family: an alternative to gamma and Weibull, “Biometrical Journal”, 43(1), pp. 117-130.

Lindley, D.V. 1980. Approximate Bayesian Methods, Trabajos de Estadistica Y de Investigacion Operativa, vol.31, pg:223-245.

Mudholkar, G.S., Srivastava, D.K. (1993), Exponentiated Weibull family for analyzing bathtub failure rate data, “IEEE Transactions on Reliability”, 42, pp. 299-302.

Mudholkar, G.S. and Hutson, A.D. (1996). The Exponentiated Weibull family: Some properties and a ood data application. Commun. Statist.-Theory Meth. 25 , 3059-3083.

Nadarajah.S., Cordeiro, G.M. and Ortega, E.M.M. (2013). Exponentiated Weibull Distribution: a survey, Statistical Papers 54.3 : 839-877

Nadarajah.S., and Gupta, A.K (2005). On the moments of the Exponentiated Weibull Distribution, Communications in statistics-theory and methods, 34, 253-256.

Nassar, M.M., Eissa, F.H. (2003). On the Exponentiated Weibull Distribution, Volume 32, Issue 7, 1317-1336.

Nassar, M.M., Eissa, F.H. (2004). Bayesian estimation for the exponentiated Weibull model, Communications in Statistics – Theory and Methods, 33, 2343- 2362.

Pal, M., Ali, M.M., Woo ,J. 2006. Exponentıated Weıbull Dıstrıbutıon. STATISTICA, anno LXVI, n. 2.

Rajarshi, M. B. & Rajarshi, S. (1988) Bathtub distributions: A review, Communications in Statistics A: Theory and Methods, 17, 2597-2621.

Salem, A.M., Abo-Kasem,O.E. (2011). Estimation for the Parameters of the Exponentiated Weibull Distribution Based on Progressive Hybrid Censored Samples, Int. J. Contemp. Math. Sciences, Vol. 6, no. 35, 1713 – 1724.

Saraçoglu, B., Asgharzadeh,A., Kazemi,M., Kınacı, İ., Akdam, N. (2014), Statistical Inference For The Generalızed Gompertz Distribution, 9-th International Statistics Day Symposium, Antalya, Turkey.

Singh, U., Gupta, P.K., Upadhaya, S.K. (2002)., Estimation of exponentiated Weibull shape parameters under LINEX loss function, Communications in Statistics – Simulation, 31(4) , 523-537.

Tierney, L., Kadane, J.B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the american statistical association 81.393: 82-86.