Applications of Exponentiated Moment Exponential Distribution Based on Dual Generalized Order Statistics

Dual generalized order statistics includes reversed order statistics, lower k-records and lower Pfeifer records. Therefore, the study of characteristics of dual generalized order statistics are of special interest. Pawlas and Szynal (2001) first proposed the concept of dual generalized order statistics (dgos) where in the study of distributional properties of random variables by using the inverse image of gos is popularly known as dual generalized order statistics. Burkschat et al. (2003) further studied this concept in a systematic manner. In this paper, an attempt has been made to derive the exact expression for single as well as for product moments of dual generalized order statistics from exponentiated moment exponential distribution and then results are deduced to reverse order statistics and lower record values. Further, the mean based on dual generalized order statistics and first & second moments based on order statistics from exponentiated moment exponential distribution are computed. Also, we have obtained maximum likelihood estimators of the model parameters based on order statistics. And finally, we have done real data analysis for exhibiting the applications of exponentiated moment exponential distribution in real-world.

Dual generalized order statistics, order statistics, exponentiated moment exponential distribution, single & product moments and maximum likelihood estimation.

1. Ahsanullah, M. 2004. “A Characterization of the Uniform Distribution by Dual Generalized Order Statistics.” Commun Statist Theory Methods 33: 2921–28. [Google Scholar] [Crossref]

2. Ahsanullah, M. 2005. “On Lower Generalized Order Statistics and a Characterization of Power Function Distribution.” Stat Methods 7: 16–28. [Google Scholar] [Crossref]

3. Akhter, Z., S. M. T. K. MirMostafaee, and E. Ormoz. 2022. “On the Order Statistics of Exponentiated Moment Exponential Distribution and Associated Inference. Journal of Statistical Computation and Simulation.” Journal of Statistical Computation and Simulation 6: 1322–46. https://doi.org/10.1080/00949655.2021.1991927. [Google Scholar] [Crossref]

4. Balakrishnan, N., and A. C. Cohen. 1991. Order Statistics and Inference Estimation Methods. Academic Press, San Diego. [Google Scholar] [Crossref]

5. Burkschat, M., Cramer, E., and Kamps, U. (2003). “Dual generalized order statistics.” Metron, LXI:13–26. [Google Scholar] [Crossref]

6. David, H., and H. N. Nagaraja. 2003. Order Statistics. In Metron. Wiley. [Google Scholar] [Crossref]

7. Gradshteyn, I. S., and I. M. Ryzhik. 2000. Table of Integrals, Series, and Products. Sixth edition. Academic Press. [Google Scholar] [Crossref]

8. Gupta, R. D., and D. Kundu. 1999. “Generalized Exponential Distributions.” Aust N Z J Stat 41: 173–88. [Google Scholar] [Crossref]

9. Hasnain, S. A. 2013. Exponentiated Moment Exponential Distributions [Dissertation]. National College of Business Administration; Economics. [Google Scholar] [Crossref]

10. Kamps, U. 1995. A Concept of Generalized Order Statistics. B.G. Teubner Stuttgart. [Google Scholar] [Crossref]

11. Khan, M. A. R., R. U. Khan, and B. Singh. 2019a. “Relations for Moments of Dual Generalized Order Statistics from Exponentiated Rayleigh Distribution and Associated Inference.” Journal of Statistical Theory and Applications 18 (2019a): 402–15. [Google Scholar] [Crossref]

12. Khan, M. A. R., R. U. Khan, and B. Singh. 2019b. “Moments of Dual Generalized Order Statistics from Two Parameters Kappa Distribution and Characterization.” J Appl Probab Stat 14 (2019b): 85–101. [Google Scholar] [Crossref]

13. Khan, M. J. S., and A. Sharma. 2016. “Generalized Order Statistics from Chen Distribution and Its Characterization.” Journal of Statistics Applications & Probability 5(1): 123–28. [Google Scholar] [Crossref]

14. Khan, M. J. S., and A. Sharma. 2018. “Shannon Entropy and Characterization of Nadarajah and Haghighi Distribution Based on Generalized Order Statistics.” Journal of Statistics: Advances in Theory and Applications 19(1): 43–69. [Google Scholar] [Crossref]

15. Khan, M. J. S., A. Sharma, and S. Iqrar. 2019. “On Moments of Lindley Distribution Based on Generalized Order Statistics.” American Journal of Mathematical and Management Sciences 39(3): 214–33. [Google Scholar] [Crossref]

16. Nadarajah, S., and S. Kotz. 2006. “The Exponentiated Type Distributions.” Acta Appl Math 92: 97–111. [Google Scholar] [Crossref]

17. Pawlas, P. and Szynal, D. (2001). “Recurrence relations for single and product moments of lower generalized order statistics from the inverse weibull distributions.” Demonstratio Math, XXXIV:353–358. [Google Scholar] [Crossref]

18. Shawky, I., and R. A. Bakoban. 2008. “Characterization from Exponentiated Gamma Distribution Based on Record Values.” Journal of Statistical Theory and Applications 7: 263–78. [Google Scholar] [Crossref]

19. Singh, B., I. Alam, A. A. Rather, and A. Alam. 2023(b). “Linear Combination of Order Statistics of Exponentiated Nadarajah–Haghighi Distribution and Their Applications.” Lobachevskii J Math 44 (2023(b)): 4839–48. https://doi.org/https://doi.org/10.1134/S1995080223110318. [Google Scholar] [Crossref]

20. Singh, B., R. U. Khan, and A. N. Khan. 2022. “Moments of Dual Generalized Order Statistics from Topp Leone Weighted Weibull Distribution and Characterization.” Ann. Data. Sci. 9: 1129–48. https://doi.org/https://doi.org/10.1007/s40745-021-00324-1. [Google Scholar] [Crossref]

21. Singh, B., A. Sharma, and A. N. Khan. 2023(a). “Relations for Moments of Log Kumaraswamy Distribution Based on Generalized Order Statistics and Associated Inferences.” Applied Mathematics E-Notes 23 (2023(a)): 516–27. [Google Scholar] [Crossref]