Main Article Content

Abstract

This paper aims to develop a new class of distributions, namely, type II exponentiated half-logistic Topp-Leone power series (TIIEHL-TL-GPS) class of distributions. Some important properties including moments, quantiles, moment generating function, entropy and maximum likelihood estimates are derived. A simulation is conducted study to evaluate the consistency of the maximum likelihood estimates. We also present three real data examples to illustrate the usefulness of the new class of distributions. Results shows that the proposed model performs better than nested and several non-nested models on selected data sets

Keywords

Topp-Leone Power series Logarithmic Distribution Maximum Likelihood Estimation

Article Details

How to Cite
Moakofi, T., Oluyede, B., & Chipepa, F. (2021). Type II Exponentiated Half-Logistic-Topp-Leone-G Power Series Class of Distributions with Applications: Type II Exponentiated Half-Logistic-Topp-Leone-G Power Series . Pakistan Journal of Statistics and Operation Research, 17(4), 885-909. https://doi.org/10.18187/pjsor.v17i4.3775

References

  1. Al-Babtain, A. A., Elbatal, I., Chesneau, C., and Elgarhy, M. (2020). Sine Topp-Leone-G Family of Distributions: Theory and Applications. Open Physics, 18(1), 574-593.
  2. Aldahlan, M. A., Jamal, F., Chesneau, C., Elbatal, I., and Elgarhy, M. (2020). Exponentiated Power Generalized Weibull Power Series Family of Distributions: Properties, Estimation and Applications. PloS one, 15(3), e0230004.
  3. Alizadeh, M., Cordeiro, G. M., De Brito, E., and Dem{'e}trio, C. G. B. (2015). The Beta Marshall-Olkin Family of Distributions. Journal of Statistical Distributions and Applications, 2(1), 1-18.
  4. Al-Mofleh, H., Elgarhy, M., Afify, A., and Zannon, M. (2020). Type II Exponentiated Half Logistic Generated Family of Distributions with Applications. Electronic Journal of Applied Statistical Analysis, 13(2), 536-561.
  5. Bantan, R. A., Jamal, F., Chesneau, C., and Elgarhy, M. (2020). Type II power Topp-Leone Generated Family of Distributions with Statistical Inference and Applications. Symmetry, 12(1), 75.
  6. Barlow, R. E., Toland, R. H., and Freeman, T. (1984). A Bayesian Analysis of Stress-rupture Life of Kevlar 49/epoxy Spherical Pressure Vessels. In Proc. Conference on Applications of Statistics, Marcel Dekker, New York.
  7. Bekker, A., Roux, J. J. J., and Mosteit, P. J. (2000). A Generalization of the Compound Rayleigh Distribution: using a Bayesian Method on Cancer Survival Times. Communications in Statistics-Theory and Methods, 29(7), 1419-1433.
  8. Bourguignon, M., Silva, R. B., and Cordeiro, G. M. (2014). The Weibull-G Family of Probability Distributions. Journal of data science, 12(1), 53-68.
  9. Cordeiro, G. M. and Silva, R. B. (2014). The Complementary Extended Weibull Power Series Class of Distributions. {Ciência e Natura} 36(3).
  10. Eugene, N., Lee, C., and Famoye, F. (2002). Beta-normal Distribution and its Applications. Communications in Statistics-Theory and methods, 31(4), 497-512.
  11. Flores, J., Borges, P., Cancho, V. G., and Louzada, F. (2013). The Complementary Exponential Power Series Distribution. {Brazilian Journal of Probability and Statistics,} 27(4), 565-584.
  12. Gradshetyn, I. S., and Ryzhik, I. M. (2000). Tables of Integrals, Series and Products, Sixth Edition, Academic Press, San Diego.
  13. Hamedani, G. G., Rasekhi, M., Najibi, S., Yousof, H. M., and Alizadeh, M. (2019). Type II General Exponential Class of Distributions. Pakistan Journal of Statistics and Operation Research, 15(2), 503-523.
  14. Jamal, F., Chesneau, C., and Elgarhy, M. (2020). Type II General Inverse Exponential Family of Distributions. Journal of Statistics and Management Systems, 23(3), 617-641.
  15. Johnson, N. L., Kotz, S., and Balakrishnan, N. (1994). Continuous Distributions, Volume 1, John Wiley & Sons, New York, NY.
  16. Makubate, B., Moakofi, T., and Oluyede, B. (2021). A New Generalized Lindley-Weibull Class of Distributions: Theory, Properties and Applications. Mathematica Slovaca, vol. 71, no. 1, pp. 211-234. https://doi.org/10.1515/ms-2017-0462
  17. Morais, A. L. and Barreto-Souza, W. (2011). A Compound Class of Weibull and Power Series Distributions. {Computational Statistics and Data Analysis,} 55(3), 1410-1425.
  18. Murthy, D. P., Xie, M., and Jiang, R. (2004). Weibull Models. New York: John Wiley and Sons.
  19. Nadarajah, S., Cordeiro, G. M., and Ortega, E. M. (2015). The Zografos-Balakrishnan-G Family of Distributions: mathematical properties and applications. Communications in Statistics-Theory and Methods, 44(1), 186-215.
  20. Oluyede, B., Chipepa, F. and Wanduku, D. (2021). The Odd Weibull-Topp-Leone-G Power Series Family of Distributions: Model, Properties and Applications. The Journal of Nonlinear Sciences and Applications, 14(4), 268-286.
  21. Oluyede, B., Fagbamigbe, A., Mashabe, B., Makubate, B., and Wanduku, D. (2020). The Exponentiated Generalized Power Series Family of distributions: Theory Properties and Applications. {Heliyon,} 6(8).
  22. Oluyede, B. O., Mdlongwa, P., Makubate, B., and Huang, S. (2019). The Burr-Weibull Power Series Class of Distributions. {Austrian Journal of Statistics,} 48, 1-13.
  23. Oluyede, B. O., Moakofi, T., Chipepa, F. and Makubate, B., (2020). A New Power Generalized Weibull-G Family of Distributions: Properties and Applications, Journal of Statistical Modelling: Theory and Applications, 1-25.
  24. Osatohanmwen, P., Oyegue, F. O., and Ogbonmwan, S. M. (2020). The T-R {Y} Power Series Family of Probability Distributions. Journal of the Egyptian Mathematical Society, 28(1), 1-18.
  25. Rezaei, S., Sadr, B. B., Alizadeh, M., and Nadarajah, S. (2017). Topp-Leone Generated Family of Distributions: Properties and Applications. Communications in Statistics-Theory and Methods, 46(6), 2893-2909.
  26. R{'e}nyi, A. (1961). On measures of Entropy and Information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1. {The Regents of the University of California}.
  27. Sanusi, A. A., Doguwa, S. I. S., Audu, I., and Baraya, Y. M. (2020). Burr X Exponential-G Family of Distributions: Properties and Application. Asian Journal of Probability and Statistics, 7(3), 58-75.
  28. Shannon C. E. (1951). Prediction and entropy of printed english. {The Bell System Technical Journal}, 30(1), 50--64.
  29. Silva, R. B., Bourguignon, M., Dias, C. R. B. and Cordeiro, G. M. (2013). The compound class of extended Weibull power series distributions. {Computational Statistics and Data Analysis,} 58, 352-367.
  30. Silva, R. B. and Cordeiro, G. M. (2015). The Burr XII Power Series Distributions: A New Compounding Family. {Brazilian Journal of Probability and Statistics,} 29(3), 565-589.
  31. Soliman, A. H., Elgarhy, M. A. E., and Shakil, M. (2017). Type II Half Logistic Family of Distributions with Applications. Pakistan Journal of Statistics and Operation Research, 2, 245-264.
  32. Yousof, H. M., Rasekhi, M., Afify, A. Z., Ghosh, I., Alizadeh, M., and Hamedani, G. G. (2017). The Beta Weibull-G Family of Distributions: Theory, Characterizations and Applications. Pakistan Journal of Statistics, 33(2).