[Home ] [Archive]   [ فارسی ]  
:: Main :: About :: Current Issue :: Archive :: Search :: Submit :: Contact ::
Main Menu
Home::
Journal Information::
Articles archive::
For Authors::
For Reviewers::
Registration::
Ethics Considerations::
Contact us::
Site Facilities::
::
Search in website

Advanced Search
..
Receive site information
Enter your Email in the following box to receive the site news and information.
..
Indexing and Abstracting



 
..
Social Media

..
Licenses
Creative Commons License
This Journal is licensed under a Creative Commons Attribution NonCommercial 4.0
International License
(CC BY-NC 4.0).
 
..
Similarity Check Systems


..
:: ::
Back to the articles list Back to browse issues page
Estimation and Prediction in Lindley-Weibel Distribution Based on Record Data
Mehrdad Norouzi Firooz , Hossein Jabbari Khamnei , Ali Akbar Heydari *
Abstract:   (93 Views)
The aim of this paper is to develop statistical inference methods for the Lindley-Weibull distribution when only upper record values are available. Using record theory, likelihood functions for parameter estimation are derived, and maximum likelihood estimators are presented. Additionally, a method for predicting future records based on observed records is proposed. The performance of the methods is evaluated through a simulation study and an application to real flood discharge data. The results indicate that the Lindley-Weibull distribution has high flexibility in modeling record data, and the proposed inference methods have appropriate accuracy.
Keywords: Lindley-Weibull distribution, Moment, MLE, Record prediction.
Full-Text [PDF 1358 kb]   (81 Downloads)    
Type of Study: Research | Subject: Statistical Inference
Received: 2025/11/17 | Accepted: 2026/09/1
References
1. باستان، ف.، كامل میرمصطفائی، س. م. ت. (1400)، برآورديابی و پیش‌بینی براي توزيع پواسن-نمايی بر اساس ركوردها و زمان هاي بین ركورد،.مجله علوم آماري، 15(2)، 381-405. [DOI:10.52547/jss.15.2.381]
2. Ahsanullah, M., and Nevzorov, V. B. (2025). Record Statistics. In International Encyclopedia of Statistical Science (pp. 2132-2141). Berlin, Heidelberg: Springer Berlin Heidelberg. [DOI:10.1007/978-3-662-69359-9_520]
3. Aly, A. E., Barakat, H. M., and El-Adll, M. E. (2019). Prediction Intervals of the Record-Values Process. Revstat-Statistical Journal, 17 (3), 401-427.
4. Arnold, B. C., Balakrishnan, N., and Nagaraja, H. N. (2011). Records. John Wiley and Sons.
5. Balakrishnan, N., and Ahsanullah, M. (1994). Relations for Single and product Moments of Record Values from Lomax Distribution. Sankhyā: The Indian Journal of Statistics, Series B, 140-146.
6. Basak, P., and Balakrishnan, N. (2003). Maximum Likelihood Prediction of Future Record Statistic. In Mathematical and Statistical Methods in Reliability (pp. 159-571). [DOI:10.1142/9789812795250_0011]
7. Bastan F, Kamel MirMostafaee S M T (2022). Estimation and Prediction for the Poisson-Exponential Distribution Based on Records and Inter-Record Times: A Comparative Study. JSS; 15 (2) :381-405. URL: http://jss.irstat.ir/article-1-709-fa.html [DOI:10.52547/jss.15.2.381]
8. Cakmakyapan, S. and Ozel, G. (2016). The Lindley Family of Distributions: Properties and Applications. Hacettepe Journal of Mathematics and Statistics, 46 (6), 1113-1137. [DOI:10.15672/HJMS.201611615850]
9. Chandler, K. (1952). The Distribution and Frequency of Record Values. Journal of the Royal Statistical Society: Series B (Methodological), 14 (2), 220-228. [DOI:10.1111/j.2517-6161.1952.tb00115.x]
10. Choulakian, V., and Stephens, M. A. (2001). Goodness-of-Fit Tests for the Generalized Pareto Distribution. Technometrics, 43 (4), 478-484. [DOI:10.1198/00401700152672573]
11. Cordeiro, G. M., Afify, A. Z., Yousof, H. M., Cakmakyapan, S., and Ozel, G. (2018). The Lindley Weibull Distribution: Properties and Applications. Anais da Academia Brasileira de Ciências, 90 , 2579-2598. [DOI:10.1590/0001-3765201820170635] [PMID]
12. Dey, S., Dey, T., and Luckett, D. J. (2016). Statistical Inference for the Generalized Inverted Exponential Distribution Based on Upper Record Values. Mathematics and Computers in Simulation, 120 , 64-78. [DOI:10.1016/j.matcom.2015.06.012]
13. Doostparast, M., and Balakrishnan, N. (2013). Pareto Analysis Based on Records. Statistics, 47 (5), 1075-1089. [DOI:10.1080/02331888.2012.694440]
14. Empacher, C. (2024). Point and Interval Prediction of Record Values (Doctoral Dissertation, Dissertation, RWTH Aachen University, 2024).
15. Empacher, C., Kamps, U., and Schmiedt, A. B. (2025). Prediction Intervals for Future Pareto Record Claims. European Actuarial Journal, 15 (1), 163-197. [DOI:10.1007/s13385-024-00397-1]
16. Gradshteyn, I. S., and Ryzhik, I. M. (2014). Table of Integrals, Series, and Products. Academic Press.
17. Lawless, J. F. (2011). Statistical Models and Methods for Lifetime Data. John Wiley and Sons.
18. Nevzorov, V. B. (1988). Records. Theory of Probability and Its Applications, 32 (2), 201-228. [DOI:10.1137/1132032]
19. Resnick, S. I. (1973). Record Values and Maxima. The Annals of Probability, 650-266. [DOI:10.1214/aop/1176996892]
20. Shorrock, R. W. (1973). Record Values and Inter-Record Times. Journal of Applied Probability, 10 (3), 543-555. [DOI:10.2307/3212775]
21. Zanjiran, F., and Mir Mostafaee, S. M. T. K. (2024). On Estimation and Prediction for the XLindley Distribution Based on Record Data. Reliability: Theory and Applications, 19 (2), 258-272.
Send email to the article author

Add your comments about this article
Your username or Email:

CAPTCHA


XML   Persian Abstract   Print



Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Back to the articles list Back to browse issues page
مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences

Persian site map - English site map - Created in 0.13 seconds with 45 queries by YEKTAWEB 4722