Estimating the Shape Parameter of the Exponential-Weibull Distribution using Bayesian Technique


  • Duru Faith Nick P N Duru Department of Statistics, Ahmadu Bello University Zaria, Nigeria
  • Sani Doguwa Ibrahim Department of Statistics, Ahmadu Bello University Zaria, Nigeria
  • Jamilu Garba Department of Statistics, Ahmadu Bello University Zaria, Nigeria


No additional refinement keywords


The Exponenial-Weibull Distribution (EWD) has been found to be useful in modeling and prediction of real life events. Its three parameter property makes it more flexible in modeling/accommodating dataset of different characteristics. However, Bayesian techique which is more robust and efficient in most cases, has not been used to estimate the shape parameter of this very important distribution. In view of this, Bayesian technique has been employed to estimate the shapeparameter of the distribution. The performance of the technique isassessed and compared with that of maximum likelihood using Monte-carlo simulation. One informative and two non-informative priors as well as threelossfunctionswereused for the study. The results showed that; Bayesian technique produced estimators with lower MSEs regardless of the chosen sample size and parameter value.


Ahmad, K., Ahmad, S. P. and Ahmed, A. (2016).Classical and Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution. Journal of Probability and Statistics, Volume 2016, Article ID 7581918, 8 pages

Aliyu, Y. and Yahaya, A. (2016).Bayesian estimation of the shape parameter of generalized Rayleigh distribution under non-informative prior. International Journal of Advanced Statistics and Probability, 4 (1), 1-10.

Azam, Z. and Ahmad, S. A. (2014). Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution. International Journal of Advanced Science and Technology , 65; 71-80.

Bourguignon, M., Silva, R. B. and Cordeiro, G. M. (2014). The Weibull-G family of probability distributions. Journal of Data Science, 12, 53-68.

Dey, S., and Maiti, S. S. (2010). Bayesian estimation of the parameter of Maxwell distribution under different loss functions. Journal of Statistical Theory and Practice, 4(2), 279-287.

Dey, S., Dey, T., & Maiti, S. S. (2013). Bayesian inference for Maxwell distribution under conjugate prior. Model Assisted Statistics and Applications, 8(3), 193-203.

Eraikhuemen, I. B., Bamigbala, O. A., Magaji, U. A., Yakura, B. S. and Manju, K. A. (2020a). Bayesian Analysis of Weibull-Lindley Distribution Using Different Loss Functions. Asian Journal of Advanced Research and Reports, 8(4), 28-41.

Eraikhuemen, I. B., Mohammed, F. B. and Sule, A. A. (2020b). Bayesian and Maximum Likelihood Estimation of the Shape Parameter of Exponential Inverse Exponential Distribution: A Comparative Approach. Asian Journal of Probability and Statistics, 7(2), 28-43.

Gupta, I. (2017). Estimation of Parameter And Reliability Function of Exponentiated Inverted Weibull Distribution using Classical and Bayesian Approach. International Journal of Recent Scientific Research, 8(7): 18117-18819.

Gupta, P.K. and Singh, A. K. (2017). Classical and Bayesian estimation of Weibull distribution in presence of outliers. Cogent Mathematics, 4: 1300975.

Ieren, T. G. and Oguntunde, P. E. (2018). A Comparison between Maximum Likelihood and Bayesian Estimation Methods for a Shape Parameter of the Weibull-Exponential Distribution. Asian Journal of Probability and Statistics, 1(1), 1-12.

Ieren, T. G., Chama, A. F., Bamigbala, O. A., Joel, J., Kromtit, F. M. &Eraikhuemen, I. B. (2020). On A Shape Parameter of Gompertz Inverse Exponential Distribution Using Classical and Non Classical Methods of Estimation. Journal of Scientific Research & Reports, 25(6), 1-10.

Krishna, H., & Goel, N. (2017). Maximum Likelihood and Bayes Estimation in Randomly Censored Geometric Distribution. Journal of Probability and Statistics, 2017. 12 pages

Martz, H. F. and Waller, R. A. (1982). Bayesian reliability analysis. New York, NY: John Wiley.

Preda, V., Eugenia, P. and Alina, C. (2010). Bayes Estimators of Modified-Weibull Distribution parameters using Lindley's approximation. WSEAS Transactions on Mathematics, 9 (7), 539-549.

Singpurwalla ND. Reliability and risk: A Bayesian perspective. Chichester: John Wiley, 2006.