:: Volume 14, Issue 2 (3-2018) ::
JSRI 2018, 14(2): 171-188 Back to browse issues page
Rayleigh Confidence Regions based on Record Data
Mousa Abdi 1, Akbar Asgharzadeh
1- , me.abdi@bam.ac.ir
Abstract:   (3473 Views)
This paper presents exact joint confidence regions for the parameters of the Rayleigh distribution based on record data. By providing some appropriate pivotal quantities, we construct several joint confidence regions for the Rayleigh parameters. These joint confidence regions are useful for constructing confidence regions for functions of the unknown parameters. Applications of the joint confidence regions using two environmental data sets are presented for illustrative purposes. Finally, a simulation study is conducted to study the performance of the proposed joint confidence regions.
 
 
Keywords: Joint confidence region, pivotal quantity, Rayleigh distribution, records
Full-Text [PDF 1099 kb]   (1297 Downloads)    
Type of Study: Research | Subject: General
Received: 2016/08/8 | Accepted: 2017/10/16 | Published: 2018/03/17
References
1. Ahmadi, J. and Arghami, N.R. (2003). Comparing the Fisher Information in Record Values and iid Observations. Statistics, 37, 435-441. [DOI:10.1080/02331880310001598855]
2. Ahsanullah, M. (1995). Introduction to Record Statistics, NOVA Science Publishers Inc., Huntington, New York.
3. Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1998), Records. John Wiley & Sons, New York. [DOI:10.1002/9781118150412]
4. Asgharzadeh, A. and Abdi, M. (2011). Confidence Intervals and Joint Confidence Regions for the Two-parameter Exponential Distribution based on Records. Communications of the Korean Statistical Society, 18, 102-110. [DOI:10.5351/CKSS.2011.18.1.103]
5. Asgharzadeh, A. and Azizpour, M. (2016). Bayesian Inference for Rayleigh Distribution under Hybrid Censoring. International Journal of System Assurance Engineering and Management, 7, 239-249. [DOI:10.1007/s13198-014-0313-7]
6. Asgharzadeh, A., Abdi, M. and Valiollahi, R. (2013). Analysis of Record Data from the Scaled Logistic Distribution, Journal of Statistical Research of Iran, 10, 41-62. [DOI:10.18869/acadpub.jsri.10.1.41]
7. Asgharzadeh, A., Abdi, M. and Wu, S.J. (2015). Interval Estimation for the Two-parameter Bathtub-Shaped Lifetime Distribution based on Records, Hacettepe Journal of Mathematics and Statistics, 44, 399-416.
8. Asgharzadeh, A., Abdi, M. and Nadarajah, S. (2016). Interval Estimation for Gumbel Distribution Using Climate Records, Bulletin of the Malaysian Mathematical Sciences Society, 39, 257-270. [DOI:10.1007/s40840-015-0185-2]
9. Battacharya, P. and Bhattacharjee, R. (2010). A Study on Weibull Distribution for Estimating the Parameters. Journal of Applied Quantitative Methods, 5, 234-241.
10. Chandler, K.N. (1952). The Distribution and Frequency of Record Values. Journal of Royal Statist Soc., B14, 220-228.
11. Dey, S., Dey, T. and Kundu, D. (2014). Two-parameter Rayleigh Distribution: Different Methods of Estimation. American Journal of Mathematical and Management Sciences, 33, 55-74. [DOI:10.1080/01966324.2013.878676]
12. Johnson, N.L., Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, John Wiley & Sons, New York.
13. Khan, H.M.R., Provost, S.B. and Singh, A. (2010). Predictive Inference from a Two-parameter Rayleigh Life Model Given a Doubly Censored Sample, Communications in Statistics - Theory and Methods, 39, 1237-1246. [DOI:10.1080/03610920902871453]
14. Kinanci, I., Wu, S.J. and Kus, C. (2017). Confidence Intervals and Regions for the Generalized Inverted Exponential Distribution based on Progressively Censored and Upper Record Data, REVSTAT (to appear).
15. Mirfarah, E. and Ahmadi, J. (2014). Pitman-Closeness of Preliminary Test and Some Classical Estimators based on Records from Two-parameter Exponential Distribution, Journal of Statistical Research of Iran, 11, 73-96. [DOI:10.18869/acadpub.jsri.11.1.73]
16. Nevzorov, V.B. (1988). Records, Theory of Probability and its Applications, 32, 201-228. [DOI:10.1137/1132032]
17. Raqab, M.Z. and Madi, MT. (2002). Bayesian Prediction of the Total Time on Test Using Doubly Censored Rayleigh Data. Journal of Statistical Computation and Simulation, 72, 781-789. [DOI:10.1080/00949650214670]
18. Rayleigh, J.W.S. (1880). On the Resultant of a Large Number of Vibrations of the Some Pitch and of Arbitrary Phase, Philosophical Magazine, 5-th Series, 10, 73-78.
19. Soliman, A.A. and Al-Aboud F.M. (2008). Baysian Inference Using Record Values from Rayleigh Model with Application. European Journal of Operational Research, 185, 252-272. [DOI:10.1016/j.ejor.2007.01.023]
20. Wu, S., Chen, D. and Chen, S. (2006). Baysian Inference for Rayleigh Distribution under Progressive Censored Sample. Applied Stochastic Models in Business and Industry, 26, 126-279.
21. Zakerzadeh, H., Jafari, A.A. and Karimi, M. (2016). Preliminary Test and Shrinkage Estimations of Scale Parameters for Two Exponential Distributions based on Record Values, Journal of Statistical Research of Iran, 13, 43-58. [DOI:10.18869/acadpub.jsri.13.1.3]



XML   Persian Abstract   Print



Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Volume 14, Issue 2 (3-2018) Back to browse issues page