A Comparative Study for Weighted Rayleigh Distribution
DOI:
https://doi.org/10.13052/jrss0974-8024.14112Keywords:
Weighted Rayleigh distribution, maximum likelihood estimator, Bayes estimator, data setsAbstract
In this paper, Bayesian and non-Bayesian methods are used for parameter estimation of weighted Rayleigh (WR) distribution. Posterior distributions are derived under the assumption of informative and non-informative priors. The Bayes estimators and associated risks are obtained under different symmetric and asymmetric loss functions. Results are compared on the basis of posterior risk and mean square error using simulated and real life data sets. The study depicts that in order to estimate the scale parameter of the weighted Rayleigh distribution use of entropy loss function under Gumbel type II prior can be preferred. Also, Bayesian method of estimation having least values of mean squared error gives better results as compared to maximum likelihood method of estimation.
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References
Ajami, M., & Jahanshahi, S. M. A. (2017). Parameter Estimation in Weighted Rayleigh Distribution. Journal of Modern Applied Statistical Methods, 16(2), 256–276.
Bashir, S., & Rasul, M. (2018). A New Weighted Rayleigh Distribution: Properties and Applications on Lifetime Time Data. Open Journal of Statistics, 8(3), 640–650.
Calabria, R., & Pulcini, G. (1994). An engineering approach to Bayes estimation for the Weibull distribution. Microelectronics Reliability, 34(5), 789–802.
Fisher, R.A. (1934). The Effects of Methods of Ascertainment upon the Estimation of Frequencies, Annals of Eugenics, 6, 13–25.
Gauss, C. F. (1810). Least Squares method for the Combinations of Observations. (Translated by J. Bertrand 1955). Mallet-Bachelier, Paris.
Gomes, A. E., da-Silva, C. Q., Cordeiro, G. M., & Ortega, E. M. (2014). A new lifetime model: the Kumaraswamy generalized Rayleigh distribution. Journal of statistical computation and simulation, 84(2), 290–309.
Haq, M. A. (2016). Kumaraswamy exponentiated inverse Rayleigh distribution. Mathematical theory and modeling, 6(3), 93–104.
Iriarte, Y. A., Vilca, F., Varela, H., & Gómez, H. W. (2017). Slashed generalized Rayleigh distribution. Communications in Statistics-Theory and Methods, 46(10), 4686–4699.
Lawless, J. F. (2003). Statistical models and methods for lifetime data (Vol. 362). John Wiley & Sons.
Legendre, A. M. (1805). New methods for the determination of orbits of comets. Courcier, Paris.
Merovci, F. (2013). Transmuted Rayleigh distribution. Austrian Journal of Statistics, 42(1), 21–31.
Merovci, F., & Elbatal, I. (2015). Weibull Rayleigh distribution: Theory and applications. Applied Mathematics & Information Sciences, 9(4), 2127–2137.
Mudasir, S., Jan, U. & Ahmad, S. P. (2019). Weighted Rayleigh Distribution Revisited Via Informative and Non-Informative Priors. Pakistan Journal of Statistics, 35(4), 321–348.
Nadarajah, S., & Kotz, S. (2006). The beta exponential distribution. Reliability engineering & system safety, 91(6), 689–697.
Norstrom, J. G. (1996). The use of precautionary loss functions in risk analysis. IEEE Transactions on reliability, 45(3), 400–403.
Rao, C. R. (1965). On discrete distributions arising out of methods of ascertainment, in classical and contagious discrete distributions. G.P. Patil, ed., Pergamon Press and Statistical Publishing Society, Calcutta, 320–332.
Rayleigh, J. (1880). On the resultant of a large number of vibrations of the same pitch and of arbitrary phase, Philosophical Magazine, 10, 73–78.
Sindhu, T. N., Aslam, M., & Feroze, N. (2013). Bayes estimation of the parameters of the inverse Rayleigh distribution for left censored data. Probstat Forum, 6, 42–59.