Main Article Content
Abstract
The researchers in applied statistics are recently highly motivated to introduce new generalizations of distributions due to the limitations of the classical univariate distributions. In this study, we propose a new family called new generalized-X family of distributions. A special sub-model called new generalized-Weibull distribution is studied in detail. Some basic statistical properties are discussed in depth. The performance of the new proposed model is assessed graphically and numerically. It is compared with the five well-known competing models. The proposed model is the best in its performance based on the model adequacy and discrimination techniques. The analysis is done for the real data and the maximum likelihood estimation technique is used for the estimation of the model parameters. Furthermore, a simulation study is conducted to evaluate the performance of the maximum likelihood estimators. Additionally, we discuss a mixture of random effect models which are capable of dealing with the overdispersion and correlation in the data. The models are compared for their best fit of the data with these important features. The graphical and model comparison methods implied a good improvement in the combined model.
Keywords
Article Details

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.
References
- Ahmad, Z., & Hussain, Z. (2017). The new extended flexible Weibull distribution and its applications. International Journal of Data Science and Analysis, 3(3), 18-23. DOI: https://doi.org/10.11648/j.ijdsa.20170303.11
- Andrews, D. F. and Herzberg, A. M. (2012). Data: A Collection of problems from many fields for the student and research worker. Springer Science & Business Media.
- Andrews, D. F., & Herzberg, A. M. (1985). Data: A collection of problems from many fields for the student and research worker. New York: Springer-Verlag. DOI: https://doi.org/10.1007/978-1-4612-5098-2
- Barlow, R. E., Toland, R. H., and Freeman, T. (1984). A Bayesian analysis of stress-rupture life of Kevlar/Epoxy spherical pressure vessels. Proceedings of the Canadian Conference in Applied Statistics, Edited by: Dwivedi, T. D. New York: MarcelDekker.
- Bebbington, M., Lai, C. D. and Zitikis, R. (2007). A flexible Weibull extension. Reliability Engineering and System Safety, 92, 719-726. DOI: https://doi.org/10.1016/j.ress.2006.03.004
- Breslow, N.E. and Lin, X. (1995). Bias correction in generalized linear mixed models with a single component of dispersion. Biometrika, 82, 81–91. DOI: https://doi.org/10.1093/biomet/82.1.81
- Carrasco M., Ortega E. M. and Cordeiro G. M. (2008). A generalized modified Weibull distribution for lifetime modelling. Computational Statistics and Data Analysis, 53(2), 450–62. DOI: https://doi.org/10.1016/j.csda.2008.08.023
- Chipepa, F., Oluyede, B., & Makubate, B. (2020). The odd generalized half-logistic Weibull-G family of distributions: properties and applications. Journal of Statistical Modelling: Theory and Applications, 1(1), 65-89.
- Chipepa, F., Oluyede, B., & Peter, P. O. (2021). The Burr III-Topp-Leone-G family of distributions with applications. Heliyon, 7(4), e06534. DOI: https://doi.org/10.1016/j.heliyon.2021.e06534
- Cordeiro, G. M., Ortega, E. M., & Nadarajah, S. (2010). The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute, 347(8), 1399-1429. DOI: https://doi.org/10.1016/j.jfranklin.2010.06.010
- Falgore, J. Y., & Doguwa, S. I. (2020). Kumaraswamy-odd rayleigh-g family of distributions with applications. Open Journal of Statistics, 10(04), 719. DOI: https://doi.org/10.4236/ojs.2020.104045
- Famoye, F., Lee, C. and Olumolade, O. (2005). The beta-Weibull distribution. Journal of Statistical Theory and Applications, 4(2), 121–36.
- Galton, F. (1883). Enquiries into Human Faculty and its Development. London: Macmillan & Company. DOI: https://doi.org/10.1037/14178-000
- Glanzel, W. (1987). A characterization theorem based on truncated moments and its application to some distribution families. In Mathematical statistics and probability theory (pp. 75-84). Springer, Dordrecht. DOI: https://doi.org/10.1007/978-94-009-3965-3_8
- Glanzel, W. (1990). Some consequences of a characterization theorem based on truncated moments. Statistics,21(4), 613-618. DOI: https://doi.org/10.1080/02331889008802273
- Hamedani, G. G. (2013). On certain generalized gamma convolution distributions II (No. 484). Technical report.
- Kassahun, W., Neyens, T., Molenberghs, G., Faes, C., & Verbeke, G. (2012). Modeling overdispersed longitudinal binary data using a combined beta and normal random-effects model. Archives of Public Health, 70(1), 1-13. DOI: https://doi.org/10.1186/0778-7367-70-7
- Marinho, P. R. D., Bourguignon, M., & Marinho, M. P. R. D. (2016). Package ’Adequacy Model’.
- Maxwell, O., Chukwu, A. U., Oyamakin, O. S., & Khaleel, M. A. (2019). The Marshall-Olkin inverse Lomax distribution (MO-ILD) with application on cancer stem cell. Journal of Advances in Mathematics and Computer Science, 1-12. DOI: https://doi.org/10.9734/jamcs/2019/v33i430186
- Molenberghs, G., Verbeke, G., Demetrio, C. G., & Vieira, A. M. (2010). A family of generalized linear models for repeated measures with normal and conjugate random effects. Statistical science, 25(3), 325-347. DOI: https://doi.org/10.1214/10-STS328
- Molenberghs, G., Verbeke, G., & Demetrio, C. G. (2007). An extended random-effects approach to modeling repeated, overdispersed count data. Lifetime data analysis, 13(4), 513-531. DOI: https://doi.org/10.1007/s10985-007-9064-y
- Molenberghs, G. and Verbeke, G. (2005). Models for Discrete Longitudinal Data. New York: Springer.
- Moors, J. J. (1988). A quantile alternative for kurtosis. Journal of the Royal Statistical Society D, 37, 25-32. http://dx.doi.org/10.2307/234. DOI: https://doi.org/10.2307/2348376
- Moss, T. R. (2004). The reliability data handbook. Professional Engineering Publishing.
- Oliveira, I. R. C. D. (2014). Modeling strategies for complex hierarchical and overdispersed data in the life sciences (Doctoral dissertation, Universidade de Sao Paulo ˜ ).
- Oluyede, Broderick. ”The gamma-Weibull-G Family of distributions with applications.” Austrian Journal of Statistics 47, no. 1 (2018): 45-76. DOI: https://doi.org/10.17713/ajs.v47i1.155
- Package ’Adequacy Model’. February 19, 2015.http://www.r-project.org.
- Sarhan, A. M. and Apaloo, J. (2013). Exponentiated modified Weibull extension distribution. Reliability Engineering and System Safety, 112, 137–144. DOI: https://doi.org/10.1016/j.ress.2012.10.013
- Silva, G. O., Ortega, E. M., & Cordeiro, G. M. (2010). The beta modified Weibull distribution. Lifetime data analysis, 16(3), 409-430. DOI: https://doi.org/10.1007/s10985-010-9161-1