Main Article Content

Abstract

This paper proposes the 4-parameter odd Lomax generalized exponential distribution for the study of engineering and COVID-19 data. The statistical and mathematical properties of this distribution such as a linear representation of the probability density function, survival function, hazard rate function, moments, quantile function, order statistics, entropy, mean deviation, characteristic function, and average residual life function are established. The estimates of parameters of the proposed distribution are obtained using maximum likelihood estimation (MLE), Maximum product spacings (MPS), least-square estimation (LSE), and Cramer-Von-Mises estimation (CVME) methods. A Monte-Carlo simulation experiment is carried out to study the MLEs. The applicability of the proposed distribution is evaluated using two real datasets related to engineering and COVID-19. All the computational work was performed in R programming software.

Keywords

Generalized exponential distribution Odd Lomax family COVID-19 Characteristic function Hazard function

Article Details

Author Biography

Vijay Kumar, DDU Gorakhpur University, Gorakhpur

Department of Mathematics and Statistics

How to Cite
Sapkota, L. P., & Kumar, V. (2022). Odd Lomax Generalized Exponential Distribution: Application to Engineering and COVID-19 data. Pakistan Journal of Statistics and Operation Research, 18(4), 883-900. https://doi.org/10.18187/pjsor.v18i4.4149

References

  1. Barreto-Souza, W., Santos, A. H., & 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
  2. Chaudhary, A. K., Sapkota, L. P., & Kumar, V. (2020a). Truncated Cauchy Power–Exponential Distribution with Theory and Applications. IOSR Journal of Mathematics (IOSR-JM), 16(6), 44-52.
  3. Chaudhary, A. K., Sapkota, L. P., & Kumar, V. (2020b). Truncated Cauchy power–inverse exponential distribution: Theory and Applications. IOSR Journal of Mathematics (IOSR-JM), 16(4), 12-23.
  4. Cheng, R. C. H., & Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society: Series B (Methodological), 45(3), 394-403. DOI: https://doi.org/10.1111/j.2517-6161.1983.tb01268.x
  5. Cordeiro, G. M., Afify, A. Z., Ortega, E. M., Suzuki, A. K., & Mead, M. E. (2019). The odd Lomax generator of distributions: Properties, estimation and applications. Journal of Computational and Applied Mathematics, 347, 222-237. DOI: https://doi.org/10.1016/j.cam.2018.08.008
  6. COVID Live - Coronavirus Statistics (2020) - Worldometer (worldometers.info) https://www. worldometers.info.
  7. Elshahhat, A., & Elemary, B. R. (2021). Analysis for Xgamma parameters of life under Type-II adaptive progressively hybrid censoring with applications in engineering and chemistry. Symmetry, 13(11), 2112. DOI: https://doi.org/10.3390/sym13112112
  8. Gómez, Y. M., Bolfarine, H., & Gómez, H. W. (2014). A new extension of the exponential distribution. Revista Colombiana de Estadística, 37(1), 25-34. DOI: https://doi.org/10.15446/rce.v37n1.44355
  9. Gupta, R. D., & Kundu, D. (2001). Generalized exponential distribution: different method of estimations. Journal of Statistical Computation and Simulation, 69(4), 315-337. DOI: https://doi.org/10.1080/00949650108812098
  10. Henningsen, A., & Toomet, O. (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics, 26(3), 443-458. DOI: https://doi.org/10.1007/s00180-010-0217-1
  11. Joshi, R. K., Sapkota, L. P., & Kumar, V. (2020). The Logistic-Exponential Power Distribution with Statistical Properties and Applications. International Journal of Emerging Technologies and Innovative Research, 7(12), 629-641.
  12. Kumar, V. (2010). Bayesian Analysis of Exponential Extension Model. J. Nat. Acad. Math, 24, 109-128.
  13. Lander, J. P. (2014). R for everyone: advanced analytics and graphics. Pearson Education.
  14. Lawless, J. F. (2011). Statistical models and methods for lifetime data. John Wiley & Sons.
  15. Lee, C., Famoye, F., & Alzaatreh, A. Y. (2013). Methods for generating families of univariate continuous distributions in the recent decades. Wiley Interdisciplinary Reviews: Computational Statistics, 5(3), 219-238. DOI: https://doi.org/10.1002/wics.1255
  16. Lemonte, A. J. (2013). A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function. Computational Statistics & Data Analysis, 62, 149-170. DOI: https://doi.org/10.1016/j.csda.2013.01.011
  17. Maiti, S. S., & Pramanik, S. (2015). Odds generalized exponential-exponential distribution. Journal of data science, 13(4), 733-753. DOI: https://doi.org/10.6339/JDS.201510_13(4).0006
  18. Mohamed, H., Mousa, S. A., Abo-Hussien, A. E., & Ismail, M. M. (2022). Estimation of the daily recovery cases in Egypt for COVID-19 using power odd generalized exponential Lomax distribution. Annals of Data Science, 9(1), 71-99. DOI: https://doi.org/10.1007/s40745-021-00336-x
  19. Mustafa, A., El-Desouky, B. S., & AL-Garash, S. (2016). Weibull generalized exponential distribution. arXiv preprint arXiv:1606.07378.
  20. Nadarajah, S., & Okorie, I. E. (2018). On the moments of the alpha power transformed generalized exponential distribution. Ozone: Science & Engineering, 40(4), 330-335. DOI: https://doi.org/10.1080/01919512.2017.1419123
  21. Nadarajah, S., & Haghighi, F. (2011). An extension of the exponential distribution. Statistics, 45(6), 543-558. DOI: https://doi.org/10.1080/02331881003678678
  22. Ogunsanya, A. S., Sanni, O. O., & Yahya, W. (2019). Exploring some properties of odd Lomax-Exponential distribution. Annals of Statistical Theory and Applications (ASTA), 1, 21-30.
  23. R Core Team (2022). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
  24. Rasekhi, M., Alizadeh, M., Altun, E., Hamedani, G. G., Afify, A. Z., & Ahmad, M. (2017). THE MODIFIED EXPONENTIAL DISTRIBUTION WITH APPLICATIONS. Pakistan Journal of Statistics, 33(5).
  25. Renyi, A. (1960). Proceedings of the 4th Berkeley Symposium on Mathematics. Statistics and Probability, 1, 547.
  26. Singh, S. K., Singh, U., & Kumar, M. (2013). Estimation of parameters of generalized inverted exponential distribution for progressive type-II censored sample with binomial removals. Journal of Probability and Statistics, 2013. DOI: https://doi.org/10.1155/2013/183652