Bayesian Approximation Techniques of Inverse Rayleigh Distribution

Kawsar Fatima, S.P. Ahmad


The present study is concerned with the estimation of inverse Rayleighdistribution using various Bayesian approximation techniques like normal approximation, and Tierney and Kadane (T-K) approximation. Different informative and non-informative priors are used to obtain the Baye’s estimate of inverse Rayleighdistribution under different approximation techniques. The simulation study has been conducted for comparison of Baye’s estimates obtained under different approximations using different priors. A real life example has also been discussed to compare the performance of these estimates.


Keywords: Bayesian estimation, prior distribution, normal approximation, T-K approximation

Cite this Article

Kawsar Fatima, Ahmad SP. Bayesian Approximation Techniques of Inverse Rayleigh Distribution. Research & Reviews: Journal of Statistics. 2018; 7(1): 50–59p.

Full Text:



Ahmed AA, Khan AA, Ahmed SP (2007). Bayesian Analysis of Exponential Distribution in S-PLUS and R Softwares. Sri Lankan Journal of Applied Statistics, 8: 95-109.

Ali, S. (2015). Mixture of the inverse Rayleigh distribution: Properties and estimation in a Bayesian framework. Applied Mathematical Modeling, 39(2): 515-530.

Ahmad SP, Ahmad, A, Khan AA (2011). Bayesian Analysis of Gamma Distribution Using SPLUS and R-software. Asian J. Math. Stat., 4: 224-233.

Soliman, A. E. Amin, and A. A. Aziz, (2010). Estimation and prediction from inverse Rayleigh distribution based on lower record values. Applied Mathematical Sciences, vol.62, pp. 3057-3066.

EI-Helbawy, A. A. and Abd-EI-Monem, (2005). Bayesian Estimation and Prediction for the Inverse Rayleigh Lifetime Distribution. Proceeding of the 40st annual conference of statistics, computer sciences and operation research, ISSR, Cairo University, 45-59.

Gharraph, M. K. (1993). Comparison of estimators of location measures of an inverse Rayleigh distribution. The Egyptian statistical Journal, 37(2): 295-309.

Mohsin and Shahbaz (2005). Comparison of Negative Moment Estimator with Maximum Likelihood Estimator of Inverse Rayleigh Distribution. Pakistan journal of statistics and operation research, Vol.1: 45-48.

Murthy, D. N. P. Xie, M. and Jiang, R. (2004). Weibull Models: (Wiley).

Rasheed, H.A. and R. kh. Aref, (2016). Bayesian Approach in Estimation of Scale Parameter of Inverse Rayleigh distribution. Mathematics and Statistics Journal, ISSN-2077-459, 2(1): 8-13.

Reshi. J. A. Ahmed and S.P. Ahmad. (2014). Bayesian analysis of scale parameter of the Generalized Inverse Rayleigh model using different loss functions. International Journal of Modern Mathematical Sciences, 10(2): 151-162.

S. Dey, (2012). Bayesian estimation of the parameter and reliability function of an inverse Rayleigh distribution. Malaysian J. of Mathematical Sciences, vol.6, pp. 113-124.

Sindhu, T. N., Aslam M., Feroze N., (2013). Bayes estimation of the parameters of the inverse Rayleigh distribution for left censored data. Prob. Stat Forum, vol. 6: 42-59.

Sultan. H, Ahmad S.P (2015). Bayesian approximation techniques of Topp-leone distribution. International Journal of Statistics and Mathematics, 2(1): 066-070.

Sultan. H, Ahmad S.P (2015). Bayesian approximation techniques for Kumaraswamy distribution. Mathematical Theory and Modeling, Vol.5, No.5, 2225-0522.

Tierney L, Kadane J (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81: 82-86.

Voda, V. G. (1972). On the inverse Rayleigh distributed random variable. Rep. Statist. App. Res., JUSE, 19: 13-21.



  • There are currently no refbacks.