The Marshall-Olkin Odd Exponential Half Logistic-G Family of Distributions: Properties and Applications

  • Broderick Oluyede Botswana International University of Science and Technology
  • Fastel Chipepa Botswana International University of Science and Technology
Keywords: Marshall-Olkin-G, Half-Logistic-G, Maximum Likelihood Estimation

Abstract

We develop a new family of distributions, referred to as the Marshall-Olkin odd exponential half logistic-G, which is a linear combination of the exponential-G family of distributions. The family of distributions can handle heavy-tailed data and has non-monotonic hazard rate functions. We also conducted a simulation study to assess the performance of the proposed model. Real data examples are provided to demonstrate the usefulness of the proposed model in comparison with several other existing models.

Author Biography

Broderick Oluyede, Botswana International University of Science and Technology
Professor of Mathematical Statistics Department of Mathematics and Statistical Sciences Botswana International University of Science and Technology

References

A. Z. Afify, E. Altun, M. Alizadeh, G. Ozel, and G. G. Hamedani, The odd exponentiated half-logistic-G family: properties, characterizations and applications, Chilean Journal of Statistics, vol. 8 no. 2 pp. 65–91, 2017.

A. Ali, S. A. Hasnain, and M. Ahmad, Modified Burr XII distribution, properties and applications, Pakistan Journal of Statistics, vol. 31 no. 6 pp. 697–708, 2015.

R. Alshkaki, A Generalized Modification of the Kumaraswamy Distribution for Modeling and Analyzing Real-Life Data, Statistics, Optimization & Information Computing, vol. 8 no. 2, pp. 521–548, 2020. https://doi.org/10.19139/soic-2310-5070-869.

A. Alizadeh, G. M. Cordeiro, E. Brito, and C. G Dem´etrio Marshall-Olkin family of distributions, Journal of Statistical Distributions and Applications, vol. 4 no. 2 pp.1–18, 2015.

A. Alizadeh, Emadi., M. Doostparast, G. M. Cordeiro, and E. M. M. Ortega, A new family of distributions: The Kumaraswamy odd log-logistic, properties and applications, Hacettepe Journal of Mathematics and Statistics, vol. 44 pp. 1491–1512, 2015.

W. Barreto-Souza and H. S. Bakouch, A new lifetime model with decreasing failure rate, statistics, A Journal of Theoretical and Applied Statistics, vol. 47 pp. 465–476, 2013.

W. Barreto-Souza, A. Lemonte, and G. M. Cordeiro, General results for the Marshall and Olkin’s family of distributions, Annals of the Brazilian Academy of Sciences, vol. 3 pp. 3–21, 2013.

M. Bourguignon, R. B. Silva, and G. M. Cordeiro, The Weibull-G family of probability distributions, Journal of Data Science, vol. 12 pp. 53–68, 2014.

S. Chakraborty, and L. Handique, The generalized Marshal-Olkin- Kumaraswamy-G family of distributions, Journal of Data Science, vol. 15 no. 3 pp. 391–422, 2017.

H. Esmaeili, F.Lak, and E. Altun, The Ristic-Balakrishnan odd log-logistic family of distributions: Properties and Applications, Statistics, Optimization & Information Computing, vol. 8 no. 1, pp. 17–35, 2020. https://doi.org/10.19139/soic-2310-5070-715

Chambers, W. Cleveland, B. Kleiner, and J. Tukey, Graphical Methods for Data Analysis, Chapman and Hall, London, 1983.

G. Chen, and N. Balakrishnan, A general purpose approximate goodness-of-fit test, Journal of Quality Technology, vol. 27 pp. 154–161, 1995.

G. M. Cordeiro, M. Alizadeh, and P. R. Diniz Marinho, The type I half-logistic family of distributions, Journal of Statistical Computation and Simulation, vol. 86 no. 4 pp. 707–728, 2016.

G. M. Cordeiro, M. Alizadeh, and E. M. M. Ortega, The exponentiated half logistic family of distributions: properties and applications, Journal of Probability and Statistics, vol. 81 pp. 1–21, 2014.

E. El-sayed, and E. Mahmoud, Kumaraswamy type I half logistic family of distributions with applications, Gazi University Journal of Science, vol. 32 no. 1 pp. 333– 349, 2019.

D. Kumar, Ratio and inverse moments of Marshall-Olkin extended Burr type III distribution based on lower generalized order statistics, Journal of Data Science, vol. 14 no. 1 pp. 53–66, 2016.

D. Kumar, N. Jain, and S. Gupta, The type I generalized half-logistic distribution based on upper record values, Journal of Probability and Statistics, Vol. 2015, 11 pages, 2015. https://doi.org/10.1155/2015/393608.

B. Lazhar, Marshall-Olkin extended generalized Gompertz distribution, Journal of Data Science, vol. 15 no. 2 pp 239–266, 2017.

L. Lepetu, B. O Oluyede, B. Makubate, S. Foya, and P. Mdlongwa, Marshall-Olkin log-logistic extended Weibull distribution: Theory, properties and applications, Journal of Data Science, vol. 15 pp. 691–722, 2017.

A. W Marshall and I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, vol. 84 no. 3 pp. 641–652, 1997.

M. Muhammad, Generalized half-logistic Poisson distributions, Communications for Statistical Applications and Methods, vol. 24 pp. 353–365, 2017.

S. Nadarajah and S. Kotz, On the alternative to Weibull function, Engineering Fracture Mechanics, vol. 74 no. 3 pp. 451–456, 2007.

S. Nadarajah and S. Kotz, The exponentiated Fr´echet distribution, interstat.statjournals.net/YEAR/2003/articles/0312001.pdf, 2003.

M. Nassar, A. Alzaatreh, M. Mead, and O. Abo-Kasem, Alpha power Weibull distribution: Properties and applications,

Communications in Statistics-Theory and Methods, vol. 46 no.20 pp. 10236–10252, 2018.

R.MPakungwati, Y.Widyaningsih, and D. Lestari, Marshall-Olkin extended inverseWeibull distribution and its application, Journal of Physics, 2018.

M. Pal, M. M. Ali, and J. Woo, Exponentiated Weibull distribution, STATISTICA, vol. anno LXVI no. 2 pp. 139–147, 2006.

M. Rafiei, A. Iranmanesh, and D. K. Nagar, A bivariate gamma distribution whose marginals are finite mixtures of gamma distributions, Statistics, Optimization & Information Computing, vol. 8 no. 4, pp. 950–971, 2020. https://doi.org/10.19139/soic-2310-5070-1001.

A. R´enyi, On measures of entropy and information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1 pp. 547–561, 1960.

M. Santos-Neo, M. Bourguignon, L. M. Zea, and A. D. C. Nascimento, The Marshall-Olkin extended Weibull family of distributions, Journal of Statistical Distributions and Applications, pp 1–9, 2018.

C. E. Shannon, Prediction and entropy of printed english, The Bell System Technical Journal, vol. 30, pp. 50–64, 1951.

R. L. Smith and J. C. Naylor, A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution, Applied Statistics, vol. 36 pp. 358–369, 1987.

K. Xu, M. Xie, L.C. Tang, and S. L. Ho, Application of neural networks in forecasting engine systems reliability, Applied Software Computing, vol. 2 no. 4 pp. 255– 268, 2003.

Published
2021-12-15
How to Cite
Oluyede, B., & Chipepa, F. (2021). The Marshall-Olkin Odd Exponential Half Logistic-G Family of Distributions: Properties and Applications. Statistics, Optimization & Information Computing, 11(2), 479-503. https://doi.org/10.19139/soic-2310-5070-938
Section
Research Articles