ESTIMATION OF PARAMETER FOR INVERSE RAYLEIGH DISTRIBUTION UNDER TYPE-I HYBRID CENSORED SAMPLES

Abstract

In reliability analysis, censoring is often preferred due to cost and time restrictions. It is well-known that a hybrid censoring scheme is a mixture of conventional type-I and type-II censoring schemes. In this study, we deal with the problem of the point and interval estimation of parameter for inverse Rayleigh distribution based on the type-I hybrid censored samples. We consider the method of maximum likelihood to estimate the parameter of inverse Rayleigh distribution by using the expectation maximization algorithm. Furthermore, the approximate confidence interval based on the maximum likelihood estimator is obtained by using Fisher information. We also performed a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimator under hybrid censoring for different sizes of samples.

Keywords

• Approximate confidence interval
• expectation maximization algorithm
• inverse Rayleigh distribution
• maximum likelihood estimation
• type-I hybrid censored samples.

References

1. ⦁ Epstein, B. (1954). Truncated life tests in the exponential case. The Annals of Mathematical Statistics, 555-564.
2. ⦁ Kundu, D. (2007). On hybrid censored Weibull distribution. Journal of Statistical Planning and Inference, 137, 2127-2142.
3. ⦁ Kundu, D., & Pradhan, B. (2009). Estimating the parameters of the generalized exponential distribution in presence of hybrid censoring. Communications in Statistics-Theory and Methods, 38, 2030-2041.
4. ⦁ Dube, S., Pradhan, B., & Kundu, D. (2011). Parameter estimation of the hybrid censored log-normal distribution. Journal of Statistical Computation and Simulation, 81, 275-287.
5. ⦁ Rastogi, M. K., & Tripathi, Y. M. (2013). Inference on unknown parameters of a Burr distribution under hybrid censoring. Statistical Papers, 54, 619-643.
6. ⦁ Rastogi, M. K., & Tripathi, Y. M. (2013). Estimation using hybrid censored data from a two-parameter distribution with bathtub shape. Computational Statistics & Data Analysis, 67, 268-281.
7. ⦁ Balakrishnan, N., & Zhu, X. (2014). On the existence and uniqueness of the maximum likelihood estimates of the parameters of Birnbaum-Saunders distribution based on type-I, type-II and hybrid censored samples. Statistics, 48, 1013-1032.
8. ⦁ Balakrishnan, N., & Kundu, D. (2013). Hybrid censoring: models, inferential results and applications. Computational Statistics & Data Analysis, 57, 166-209.

9. ⦁ Kohansal, A., Rezakhah, S., & Khorram, E. (2015). Parameter estimation of Type-II hybrid censored weighted exponential distribution. Communications in Statistics-Simulation and Computation, 44, 1273-1299.
10. ⦁ Rabie, A., & Li, J. (2018). E-Bayesian Estimation for Burr-X Distribution Based on Type-I Hybrid Censoring Scheme. International Journal of Applied Mathematics, 48.
11. ⦁ Sultana, F., Tripathi, Y. M., Rastogi, M. K., & Wu, S. J. (2018). Parameter Estimation for the Kumaraswamy Distribution Based on Hybrid Censoring. American Journal of Mathematical and Management Sciences, 1-19.
12. ⦁ Voda, R. Gh. (1972). On the inverse Rayleigh variable. Rep. Stat. Apph. Res. Juse, 19, pp. 15-21.
13. ⦁ Gharraph, M. K. (1993). Comparison of estimators of location measures of an inverse Rayleigh distribution. The Egyptian statistical Journal, 37, 295-309.
14. ⦁ El-Helbawy, A. A., & Abd-El-Monem (2005). Bayesian Estimation and Prediction for the Inverse Rayleigh Lifetimd Distribution. Proceeding of the 40st annual conference of statistics , computer sciences and operation research, ISSR, Cairo University, 45-59.
15. ⦁ Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39, 1-22.
16. ⦁ Ng, H. K. T., Chan, P. S., & Balakrishnan, N. (2002). Estimation of parameters from progressively censored data using EM algorithm. Computational Statistics & Data Analysis, 39, 371-386.
17. ⦁ Lieblein, J. and Zelen, M., (1956). Statistical investigation of the fatigue life of deep-groove ball bearing, J. Research National Bureau of Standards, 57, 273-316.