Article Sidebar

Download
PDF
Statistic
Read Counter : 326 Download : 408

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Main Article Content

Abstract

In this work, we introduce a novel generalization of the extended exponential distribution with four parameters through the Kumaraswamy family. The proposed model is referred to as the Kumaraswamy extended exponential (KwEE). The significance of the suggested distribution from its flexibility in applications and data modeling. As specific sub-models, it includes the exponential, Kumaraswamy exponential, Kumaraswamy Lindley, Lindley, extended exponential, exponentiated Lindley, gamma and generalized exponential distributions. The representation of the density function, quantile function, ordinary and incomplete moments, generating function, and reliability of the KwEE distribution are all derived. The maximum likelihood approach is used to estimate model parameters. A simulation study for maximum likelihood estimates was used to investigate the behaviour of the model parameters. A numerical analysis is performed for various sample sizes and parameter values to analyze the behaviour of estimates using accuracy measures. According to a simulated investigation, the KwEE's maximum likelihood estimates perform well with increased sample size. We provide two real-world examples utilizing applied research to demonstrate that the new model is more effective.

Keywords

Extended exponential distribution Moments Quantile Maximum likelihood technique

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following License

CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.

 

How to Cite
Hassan, A. S., Mohamed, R. E., Kharazmi, O., & Nagy, H. F. (2022). A New Four Parameter Extended Exponential Distribution with Statistical Properties and Applications . Pakistan Journal of Statistics and Operation Research, 18(1), 179-193. https://doi.org/10.18187/pjsor.v18i1.3872
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Aarset, M. V. (1987). How to identify a bathtub hazard rate. IEEE Transactions on Reliability, 36(1), 106-108. DOI: https://doi.org/10.1109/TR.1987.5222310
  2. Afify, A. Z. and Mohamed, O. A. (2020). A new three-parameter exponential distribution with variable shapes for the hazard rate: Estimation and applications. Mathematics, 8(1), 135. doi:10.3390/math8010135 DOI: https://doi.org/10.3390/math8010135
  3. Afify, A. Z., Zayed, M. and Ahsanullah, M. (2018). The extended exponential distribution and its applications. Journal of Statistical Theory and Applications, 17(2), 213-229. DOI: https://doi.org/10.2991/jsta.2018.17.2.3
  4. Barreto-Souza, W., Santos, A. H. S. and Cordeiro, G. M. (2010). The beta generalized exponential distribution. Journal of Statistical Computation and Simulation, 80(2), 159-172. DOI: https://doi.org/10.1080/00949650802552402
  5. Çakmakyapan, S. and Kadilar, G. Ö. (2014). A new customer lifetime duration distribution: the Kumaraswamy Lindley distribution. International Journal of Trade, Economics and Finance, 5(5), 441-444. DOI: https://doi.org/10.7763/IJTEF.2014.V5.412
  6. Cordeiro, G. M. and de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7), 883-898. DOI: https://doi.org/10.1080/00949650903530745
  7. Cordeiro, G. M. and Lemonte, A. J. (2011). The β-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling. Computational Statistics & Data Analysis, 55(3), 1445-1461. DOI: https://doi.org/10.1016/j.csda.2010.10.007
  8. Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J. and Knuth, D. E. (1996). On the Lambert W function. Advances in Computational Mathematics, 5(1), 329-359. DOI: https://doi.org/10.1007/BF02124750
  9. de Andrade, T. A. N., Bourguignon, M. and Cordeiro, G. M. (2016). The exponentiated generalized extended exponential distribution. Journal of Data Science, 14(3), 393-413. DOI: https://doi.org/10.6339/JDS.201607_14(3).0001
  10. Elbatal, I., Louzada, F. and Granzotto, D. C. T. (2018). A New Lifetime Model: The Kumaraswamy extension exponential distribution. Biostatistics and Bioinformatics, 2, 1-9. DOI: https://doi.org/10.31031/OABB.2018.02.000527
  11. Gómez, Y., Bolfarine, H. and Gómez, H. W. (2014). A new extension of the exponential distribution. Revista Colombiana de Estad´ıstica, 37, 25-34. DOI: https://doi.org/10.15446/rce.v37n1.44355
  12. Gupta, R. D. and Kundu, D. (1999). Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173-188. DOI: https://doi.org/10.1111/1467-842X.00072
  13. Gupta, R. D. and Kundu, D. (2001). Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 43(1), 117-130. DOI: https://doi.org/10.1002/1521-4036(200102)43:1<117::AID-BIMJ117>3.0.CO;2-R
  14. Hassan, A. S., Mohamd, R. E., Elgarhy, M. and Fayomi, A. (2018). Alpha power transformed extended exponential distribution: properties and applications. Journal of Nonlinear Sciences and Applications, 12(4), 62-67. DOI: https://doi.org/10.22436/jnsa.012.04.05
  15. Jodrá, P. (2010). Computer generation of random variables with Lindley or Poisson-Lindley distribution via the Lambert W function. Mathematics and Computers in Simulation, 81(4), 851-859. DOI: https://doi.org/10.1016/j.matcom.2010.09.006
  16. Merovci, F. (2013). Transmuted exponentiated exponential distribution. Mathematical Sciences and Applications E-Notes, 1(2), 112-122.
  17. Nadarajah, S. and Haghighi, F. (2011). An extension of the exponential distribution. Statistics, 45(6), 543-558. DOI: https://doi.org/10.1080/02331881003678678
  18. Nadarajah, S. and Kotz, S. (2008). Strength modeling using Weibull distributions. Journal of mechanical science and technology, 22(7), 1247-1254. DOI: https://doi.org/10.1007/s12206-008-0426-5
  19. Nadarajah, S., Bakouch, H. S. and Tahmasbi, R. (2011). A generalized Lindley distribution. Sankhya B, 73(2), 331-359. DOI: https://doi.org/10.1007/s13571-011-0025-9
  20. Nassar, M., Kumar, D., Dey, S., Cordeiro, G. M. and Afify, A. Z. (2019). The Marshall-Olkin alpha power family of distributions with applications. Journal of Computational and Applied Mathematics, 351, 41-53. DOI: https://doi.org/10.1016/j.cam.2018.10.052
  21. Navarro, J., Franco, M. and Ruiz, J. (1998). Characterization through moments of the residual life and conditional spacings. SankhyÄ: The Indian Journal of Statistics, Series A, 60, 36-48.
  22. Rasekhi, M., Alizadeh, M., Altun, E., Hamedani, G., Afify, A. Z. and Ahmad, M. (2017). The modified exponential distribution with applications. Pakistan Journal of Statistics, 33(5), 383-398.
  23. Ristić, M. M. and Balakrishnan, N. (2012). The gamma-exponentiated exponential distribution. Journal of Statistical Computation and Simulation, 82(8), 1191-1206. DOI: https://doi.org/10.1080/00949655.2011.574633
  24. Zakerzadeh, H. and Dolati, A. (2009). Generalized Lindley distribution. Journal of Mathematical Extension, 3, 13-25.