Some Bayes Estimators for Maxwell Distribution by Using New Loss Function


  • Huda A. Rasheed Department of Mathematics, Collage of Science, Mustansiriyah University
  • Zainab N. Khalifa Department of Mathematics, Collage of Science, Mustansiriyah University



Maxwell distribution, Bayesian estimations, New loss Function, Jefferys prior and Inverted Levy prior, Mean squared error.


In the current study, we have been derived some Bayesian estimations of the scale parameter of Maxwell distribution using the New loss function (NLF) which it called Generalized weighted loss function, assuming non-informative prior, namely, Jefferys prior and information prior, represented by Inverted Levy prior. Based on Monte Carlo simulation method, those estimations are compared depending on the mean squared errors (MSE's). The results show that, the behavior of Bayesian estimation under New loss function using Inverted Levy prior when (k=0, c=3) is the better behavior than other estimates for all cases.


Maxwell, J. "On the Dynamical Theory of Gases". Presented to the meeting of the British Association for the Advancement of Science, Sep.; Phil. Mag. 19:434-36, in: Scientific Letters, Vol. I.(pg.616). 1860.

Tyagi and Bhattacharya. "Bayes estimation of the Maxwell's velocity distribution function". Statistica, 29(4): 563-567. 1989.

Chaturvedi, A. and Rani, U. "Classical and Bayesian Reliability estimation of the generalized Maxwell failure distribution". Journal of Statistical Research, 32, 113–120. 1998.

Howlader, H. A. and Hossain, A. " Bayesian prediction intervals for Maxwell parameters". Matron, LVI(1-2), 97–105. 1998.

Hartigan, J. "Invariant prior distributions". Annals of Mathematical Statistics, 35, 836–845. 1964. CrossRef

Podder, C. K. and Roy, M. K. " Bayesian Estimation of the Parameter of Maxwell Distribution undermlINEX Loss Function". Journal of Statistical Studies, 23, 11-16. 2003.

Bekker, A. and Roux, J.J.. "Reliability characteristics of the Maxwell distribution: A Bayes estimation study". Comm. Stat. (Theory & Math.), 34(11): 2169 - 2178. 2005.

Krishna and Malik, "Reliability estimation in Maxwell distribution with Type-II censored data". Int. Journal of Quality and Reliability management, 26 (2): 184 – 195. 2009. CrossRef

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

Krishna, H and Malik, M. " Reliability estimation in Maxwell distribution with progressively Type-II censored data". Journal of Statistical Computation and Simulation, 82(4), 623-641. 2012. CrossRef

Dey, S., Dey, T. and Maiti, S. S., "Bayesian inference for Maxwell distribution under conjugate prior". Model Assisted Statistics and Applications, 8, 193–203. 2013.

Rasheed. "Minimax Estimation of The Parameter of the Maxwell Distribution under Quadratic loss function". Journal of Al-Rafidain University College, ISSN (1681-6870), Issue No.31. 2013.

Rasheed, H.A. and Khalifa, Z.N. "Bayes Estimators for the Maxwell Distribution under Quadratic Loss Function Using Different Priors". Australian Journal of Basic and Applied Sciences, 10(6), pp.97-103. 2016.

Rasheed and Khalifa, Z,N.. "Semi-Minimax Estimators of Maxwell Distribution under New Loss Function". Mathematical and Statistics Journal, ISSN-2077-459,2(3), pp.16-22. 2016.

Rasheed and AL-Shareefi. "Bayes Estimator for the Scale Parameter of Laplace distribution under a Suggested Loss Function". International Journal of Advanced Research, Volume 3, Issue 3, 788-796. 2015.

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

Sindhu, T., N; Aslam M. "Bayesian Estimation on the Proportional Inverse Weibul Distribution under Different Loss Functions". Advances in Agriculture, Science and Engineering Research,vol.3(2), pp.641-655. 2013.




How to Cite

H. A. Rasheed and Z. N. Khalifa, “Some Bayes Estimators for Maxwell Distribution by Using New Loss Function”, MJS, vol. 28, no. 1, pp. 103–111, Nov. 2017.