ESTIMATION OF THE SHAPE PARAMETER OF GENERALIZED RAYLEIGH DISTRIBUTION UNDER CONJUGATE PRIOR

Yakubu Aliyu, Abubakar Yahaya

Abstract


Modeling of real life scenario help us to better understand and explain unforeseen eventualities when they take place, thereby enabling us to reproduce such a scenario on a large and/ or on a simplified scale aimed at describing critical parts of the phenomenon. Generalized Rayleigh Distribution can be used quiet effectively in modeling real life scenario. Every distribution model has a set of parameters that needs to be estimated. In this work, a Bayesian estimate of the shape parameter of Generalized Rayleigh Distribution was considered under the assumption of conjugate (gamma) prior. The Bayes estimates were obtained under both symmetric and asymmetric loss functions. The performances of these estimates were compared using Monte Carlo simulation. It is observed that the estimates under the asymmetric loss function slightly perform better than those under the symmetric loss function.


Full Text:

PDF

References


Abdel-Hady, D. H. (2013). Bivariate Generalized Rayleigh Distribution. Journal of Applied Sciences Research, 9 (9), 5403-5411.

Al – Kanani, H. I., & Abbas, S. J. (2014). Non-Bayesian and Bayesian Estimation for Generalized Rayleigh Distribution. International Journal of Modern Mathematical Sciences, 10 (2), 103-115.

AL- Naqeeb, A. A., & Hamed, A. M. (2009). Estimation of the Two Parameters for Generalized Rayleigh Distribution Function Using Simulation Technique. IBN AL- HAITHAM Journal FOR PURE & APPL. SC I. , 22 (4).

Ana, P., Betsabé, B., & Gauss, M. C. (2013). The beta Weibull Poisson distribution. Chilean Journal of Statistics , 4 (2), 3–26.

Burr, I. W. (1942). Cumulative Frequency Distribution. Annual of Mathematical Statistics, 13, 215-232.

Dey, D. K., Ghosh, M., & Srinivasan, C. (1987). Simultaneous estimation of parameters under entropy loss. Journal of Statistical Planning and Inference 15, 347-363.

Dey, D. K. & Liao Liu, P. (1992). On comparison of estimators in a generalized life model. Microelectronic Reliability 32, 207-221

Hamdy, M. S., & Mahmoud, A. S. (2014). The Generalized Weibull-Exponential Distribution: Properties and Applications. International Journal of Statistics and Applications , 4 (2), 102-112

Kundu, D., & Raqab, M. Z. (2005). Generalized Rayleigh distribution: different methods of estimations. Computational Statistics & Data Analysis, 49, 187 – 200.

Lio, Y. L., Chen, D.-G., & Tsai, T.R. (2011). Parameter Estimations for Generalized Rayleigh Distribution under Progressively Type-I Interval Censored Data. American Open Journal of Statistics , 46-57.

Mahdi, S. (2006). Improved Parameter Estimation in Rayleigh Model. Metodološki zvezki, 3 (1), 63-74.

Norstrom, J. G. (1996). The use of precautionary loss functions in risk analysis. IEEE Trans. Reliab., 45 (3), 400–403.

Pak, A., Parham, A. G., & Saraj, M. (2013). On Estimation of Rayleigh Scale Parameter under Doubly Type-II Censoring from Imprecise Data. Journal of Data Science , 305-322.

Pathak, A., & Chaturvedi, A. (2014). Estimation of the reliability function for two-parameter exponentiated Rayleigh or Burr type X distribution. Statistics Optimization and Information Computing, 305–322.

Raqab, Z. Mohammad & Kundu, Debasis. (2003). Burr Type X Distribution: Revisited. http://kundu@iitk.ac.in.

Raqab, Z. M., & Kundu, D. (2005). Comparison of Different Estimators of P[Y < X ] for a Scaled Burr Type X Distribution. Commun. Statist. -Simul. Comp., 34, 465 – 483.

Samaila, Mahdi & Myrtene Cenac. (2006). Estimating and Assessing the parameters of the logistic and Rayleigh distribution from three methods of estimation. Carrib. J. Math. comput. sci 13, 25-34.

Surles, J.G., and Padgett, W.J.. (2001). Inference for reliability and stress-strength for a scaled Burr Type X distribution. Lifetime Data Anal. 7, 187–200.

Surles, J.G., & Padgett, W.J.. (2004). Some properties of a scaled Burr type X distribution. J. Statist. Plann. Inference.


Refbacks

  • There are currently no refbacks.