THERMAL SCIENCE
International Scientific Journal
ESTIMATION AND PREDICTION OF TWO RAYLEIGH LIFETIME DISTRIBUTIONS UNDER JOINT CENSORING SCHEME
ABSTRACT
Comparative life tests of a life product have received considerable attention in the past few years for measuring the relative merits of a product in competing duration. In this paper, we are adopting the problem of estimation and prediction of Rayleigh lifetime distributions under joint Type-I censoring scheme. The point and interval estimation is formulated with maximum likelihood and the Bayes methods for the unknown parameters. Also, Bayesian approach is applied in viewpoint both point and interval prediction. The results of estimation and prediction are discussed through analysis the set of real data and bulding Monte-Carlo simulation studies. Finally, we built a numerical discussion of the most important results and future recommendations.
KEYWORDS
PAPER SUBMITTED: 2022-08-20
PAPER REVISED: 2022-10-17
PAPER ACCEPTED: 2022-11-04
PUBLISHED ONLINE: 2023-01-21
- Balakrishnan, N. Aggarwala, R., Progressive Censoring: Theory, Methods and Applications, Birkhuser, Boston, Mass., USA, 2000
- Balakrishnan, N., Progressive Censoring Methodology: An Appraisal (with Discussions), Test, 16 (2007), June, pp. 211-296
- Kundu, D., Bayesian Inference and Life Testing Plan for Weibull Distribution in Presence of Progressive Censoring, Technometrics, 50 (2008), 2, pp. 144-154
- Soliman, A. A., et al., Estimation of the Parameters of Life for Gompertz Distribution Using Progressive First-Failure Censoring Data, Computational Statistics and Data Analysis, 56 (2012), 8, pp. 2471-2485
- Rao, U. V. R., et al., Contributions to the Theory of Rank Order Statistics: The Two-Sample Censored Case, Ann Math Stat, 31 (1960), 2, pp. 415-426
- Basu, A. P., On a Generalized Savage Statistic with Applications to Life Testing, Ann Math Stat, 39 (1976), 5, pp. 1591-1604
- Johnson, R. A., Mehrotra, K. G., Locally Most Powerful Rank Tests for the Two-Sample Problem with Censored Data, Ann Math Stat, 43 (1972), 3, pp. 823-831
- Mehrotra, K. G., Johnson, R. A., Asymptotic Sufficiency and Asymptotically Most Powerful Tests for the Two Sample Censored Situation, Ann Stat, 4 (1976), 3, pp. 589-596
- Bhattacharyya, G. K., Mehrotra, K. G., On Testing Equality of Two Exponential Distributions under Combined Type-II Censoring, Journal Am Stat Assoc, 76 (1981), 376, pp. 886-894
- Mehrotra, K. G., Bhattacharyya, G. K., Confidence Intervals with Jointly Type-II Censored Samples from Two Exponential Distributions, Journal Am Stat Assoc, 77 (1982), 378, pp. 441-446
- Balakrishnan, N., Rasouli, A., Exact Likelihood Inference for Two Exponential Populations under Joint Type-II Censoring, Comput Stat Data Anal, 52 (2008), 5, pp. 2725-273
- Shafaya, A. R., et al., Bayesian Inference Based on a Jointly Type-II Censored Sample from Two Exponential Populations, Journal of Statistical Computation and Simulation, 84 (2014), 11, pp. 2427-2440
- Al-Matrafi, B. N., Abd-Elmougod, G. A., Statistical Inferences with Jointly Type-II Censored Samples from Two Rayleigh Distributions, Global Journal of Pure and Applied Mathematics, 13 (2017), 12, pp. 8361-8372
- Algarni, A., et al., Two Compound Rayleigh Lifetime Distributions in Analyses the Jointly Type-II Censoring Samples, Journal of Mathematical Chemistry, 58 (2019), Aug., pp. 950-966
- Mondal, S., Kundu, D., Bayesian Inference for Weibull Distribution under the Balanced Joint Type-II Progressive Censoring Scheme, American Journal of Mathematical and Management Sciences, 39 (2019), 1, pp. 56-74
- Mondal, S., Kundu, D., Inferences of Weibull Parameters under Balance Two Sample Type-II Progressive Censoring Scheme, Quality and Reliability Engineering International, 36 (2020), 5, pp. 1-17
- Almarashi, A. M., et al., Inferences for Joint Hybrid Progressive Censored Exponential Lifetimes under Competing Risk Model, Mathematical Problems in Engineering, 2021 (2021), ID3380467
- Dyer, D. D., Whisenand, C. W., Best Linear Unbiased Estimator of the Parameter of the Rayleigh Distribution - Part I: Small Sample Theory for Censored Order Statistics, IEEE Transactions on Reliability, 22 (1973), 1, pp. 27-34
- Dyer, D. D., Whisenand, C. W., Best Linear Unbiased Estimator of the Parameter of the Rayleigh Distribution - Part II: Optimum Theory for Selected Order Statistics, IEEE Transactions on Reliability, 22 (1973), 4, pp. 229-231
- Polovko, A. M., Fundamentals of Reliability Theory, Academic Press, New York, USA, 1986
- Algarni, A., et al.,Two Compound Rayleigh Lifetime Distributions in Analyses the Jointly Type-II Censoring Samples, Journal of Mathematical Chemistry, 58 (1968), Aug., pp. 950-966
- Harter, H. L., Moore, A. H., Point and Interval Estimators, Based on m Order Statistics, for the Scale Parameter of a Weibull Population with Known Shape Parameter, Technometrics, 7 (1965), 3, pp. 405-422
- Lalitha, S., Mishra, A., Modified Maximum Likelihood Estimation for Rayleigh Distribution, Communications in Statistics, Theory and Methods, 25 (1996), 2, pp. 389-401
- Kong, F., Fei, H., Limits Theorems for the Maximum Likelihood Estimate under General Multiply Type II Censoring, Annals of the Institute of Statistical Mathematics, 48 (1996), Dec., pp. 731-755
- Howlader, H. A., Hossain, A., On Bayesian Estimation and Prediction from Rayleigh Based on Type II Censored Data, Communications in Statistics, Theory and Methods, 24 (1995), 9, pp. 2249-2259
- Fernandez, A. J. Bayesian Inference from Type II Doubly Censored Rayleigh Data, Statistics and Probability Letters, 48 (2000), 4, pp. 393-399
- AL-Hussaini, E. K., Ahmad, A. A., On Bayes Predictive Distributions of Generalized Order Statistics, Metrika, 57 (2003), May, pp. 165-176
- AL-Hussaini, E. K., Ahmad, A. A., On Bayes Interval Prediction of Future Records, Test, 12 (2003), 1, pp. 79-99
- Kundu, D., Joarder, A., Analysis of Type-II Progressively Hybrid Censored Data, Computational Statistics and Data Analysis, 50 (2006), 10, pp. 2509-2528
- Hoel, D. G., A Representation of Mortality Data by Competing Risks, Biometrics, 28 (1972), pp. 475-488