The odd power generalized Weibull-G power series class of distributions: properties and applications

Broderick Oluyede; Thatayaone Moakofi; Fastel Chipepa

doi:10.21307/stattrans-2022-006

The odd power generalized Weibull-G power series class of distributions: properties and applications

Broderick Oluyede Botswana International University of Science and Technology, Botswana ORCID:https://orcid.org/0000-0002-9945-2255 , Thatayaone Moakofi Botswana International University of Science and Technology, Botswana ORCID:https://orcid.org/0000-0002-2676-7694 , Fastel Chipepa Botswana International University of Science and Technology, Botswana ORCID:https://orcid.org/0000-0001-6854-8740 Statistics in Transition new series, vol. 23, 2022, 1, pages: 89-108 Published online: 15 March 2022 DOI 10.21307/stattrans-2022-006 Citation: Oluyede B., Moako T., Chipepa F., (2022). The odd power generalized Weibull-G power series class of distributions: properties and applications, Statistics in Transition new series, 23(1), pp. 89–108. https://doi.org/10.21307/stattrans-2022-006

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ABSTRACT

We develop a new class of distributions, namely, the odd power generalizedWeibull-G power series (OPGW-GPS) class of distributions. We present some special classes of the proposed distribution. Structural properties, have also been derived. We conducted a simulation study to evaluate the consistency of the maximum likelihood estimates. Moreover, two real data examples on selected data sets, to illustrate the usefulness of the new class of distributions. The proposed model outperforms several non-nested models on selected data sets.

KEYWORDS

Weibull-g distribution, power series, Poisson distribution, logarithmic distribution, maximum likelihood estimation

REFERENCES

Afify, A. Z., Alizadeh, M., Zayed, M., Ramires, T. G. and Louzada, F., (2018). The Odd Log-Logistic Exponentiated Weibull Distribution: Regression Modelling, Properties, and Applications. Iranian Journal of Science and Technology, 42(4), pp. 2273–2288.

Afify, A. Z., Altun, E., Alizadeh, M., Ozel, G., and Hamedani, G. G., (2017). The Odd Exponentiated Half-Logistic-G Family: Properties, Characterizations and Applications. Chilean Journal of Statistics, 8(2), pp. 65–91.

Aldahlan, M. and Afify, A. Z., (2018). The odd exponentiated half-logistic Burr XII distribution. Pakistan Journal of Statistics and Operation Research, 14(2), pp. 305–317.

Aldahlan, M. A., Jamal, F., Chesneau, C., Elbatal, I., and Elgarhy, M., (2019). Exponentiated Power Generalized Weibull Power Series Family of Distributions: Properties, Estimation and Applications. PLoS ONE 15(3): e0230004. https://doi.org/10.1371/journal.pone.0230004.

Bourguignon, M., Silva, R. B. and Cordeiro, G. M., (2014). The Weibull-G Family of Probability Distributions. Journal of Data Science, 12, pp.53–68.

Chipepa, F., Oluyede, B. and Wanduku, D., (2020). The Exponentiated Half Logistic Odd Weibull- Topp-Leone-G Family of Distributions: Model, Properties and Applications. Journal of Statistical Modelling: Theory and Applications, 2(1), pp. 15–38.

Chipepa, F., Oluyede, B. and Makubate, B., (2020). The Odd Generalized Half-Logistic Weibull-G Family of Distributions: Properties and Applications. Journal of Statistical Modeling: theory and Applications, 1(1), 65–89.

Chipepa, F., Oluyede, B. and Makubate, B., (2020). The Topp-Leone-Marshall-Olkin-G Family of Distributions with Applications. International Journal of Statistics and Probability, 9(4), pp. 15- 32. doi:10.5539/ijsp.v9n4p15.

Chipepa, F., Oluyede, B. and Makubate, B., (2019). A New Generalized Family of Odd Lindley-G Distributions with Application. International Journal of Statistics and Probability, 8(6), pp. 1–22. doi:10.5539/ijsp.v8n6p1.

Cordeiro, G. M. and Silva, R. B., (2014). The Complementary Extended Weibull Power Series Class of Distributions. Ciencia e Natura, 36(3).

Cordeiro, G. M., Ortega, E. M. M., and da Cunha, D. C. C., (2013). The Exponentiated Generalized Class of Distributions. Journal of Data Science, 11, pp. 1–27.

Cordeiro, G. M. Ortega, E. M. M. and Nadarajaah, S., (2010). The KumaraswamyWeibull Distribution with Application to Failure Data. Journal of the Franklin Institute, 347, pp. 1399–1429.

Eugene, N., Lee, C., and Famoye, F., (2002). Beta-Normal Distribution and its Applications. Communications in Statistics: Theory and Methods, 31, pp. 497–512.

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), pp. 565–584.

Gradshetyn, I. S., and Ryzhik, I. M., (2000). Tables of Integrals, Series and Products, Sixth Edition, Academic Press, San Diego.

Jamal, F., Reyad, H. M., Nasir, M. A., Chesneau, C., Shah, M. A. A. and Ahmed S. O., (2019). Topp-Leone Weibull-Lomax Distribution: Properties, Regression Model and Applications, hal- 02270561.

Johnson, N. L., Kotz, S., and Balakrishnan, N., (1994). Continuous Distributions, Volume 1, John Wiley & Sons, New York, NY.

Makubate, B., Moakofi, T., and Oluyede, B., (2020). A new Generalized Lindley-Weibull Class of Distributions: Theory, Properties and Applications, Mathematica Slovaka, 71(1), No. 1, pp. 211– 234.

Moakofi, T., Oluyede, B., Chipepa, F and Makubate, B., (2021). Odd Power Generalized Weibull-G Family of Distributions: Properties and Applications, Journal of Statistical Modelling: Theory and Applications, 2(1), pp. 121–142.

Morais, A. L. and Barreto-Souza, W., (2011). A Compound Class of Weibull and Power Series Distributions. Computational Statistics and Data Analysis, 55(3), pp. 1410-1425.

Nichols, M. D. and Padgett, W. J. A., (2006). A Bootstrap Control Chart for Weibull Percentiles. Quality and Reliability Engineering International, 22, pp. 141–151.

Oluyede, B., Moakofi, T., Chipepa, F and Makubate, B., (2021). A New Power GeneralizedWeibull-G Family of Distributions: Properties and Applications. Journal of Statistical Modelling: Theory and Applications, 1(2), pp. 167–191.

Oluyede, B., Chipepa, F. and Wanduku, D., (2020). The Exponentiated Half Logistic-Power Generalized Weibull-G Family of Distributions: Model, Properties and Applications. Eurasian Bulletin of Mathematics, 3(3), pp. 134–161.

Oluyede, B., Chipepa, F. and Wanduku, D., (2020). The Odd Weibull-Topp-Leone-G Power Series Family of Distributions: Model, Properties and Applications. Journal of Nonlinear Sciences and Applications, 14, pp. 268–286.

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), e04653.

R Development Core Team, (2014). A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria.

Rényi, 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.

Shannon, C. E., (1951). Prediction and Entropy of Printed English, The Bell System Technical Journal, 30(1), pp. 50–64.

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, pp. 352–367.

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), pp. 565–589.