Main Article Content
Abstract
A new generalized class of distributions called the Topp-Leone-Gompertz-G Power Series (TL-Gom-GPS) distribution is presented. Some mathematical and statistical properties of the new class of distributions are explored. For this new class of distributions, we derived the quantile function, moments and generating function, probability weighted moments, distribution of the order statistics and R\'enyi entropy. The maximum likelihood technique is used for estimating model parameters and Monte Carlo simulation is conducted to show the performance of the proposed model. Finally, the usefulness and flexibility of the new class of distributions is examined by means of applications to real data sets.
Keywords
Topp-Leone
Gompertz-G
Power Series Distribution
Maximum Likelihood Estimation
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.
How to Cite
Gabanakgosi, M., & Oluyede, B. (2024). The Topp-Leone-Gompertz-G Power Series Class of Distributions with Applications: Topp-Leone-Gompertz-G Power Series Class of Distributions . Pakistan Journal of Statistics and Operation Research, 20(2), 171-195. https://doi.org/10.18187/pjsor.v20i2.4032
References
-
[1] Afify, A. Z., Alizadeh, M., Zayed, M., Ramires, T. G. and Louzada, F. (2018). The Odd Log-Logistic Exponentiated Weibull Distribution: Regression Modeling, Properties, and Applications. Iranian Journal of Science and Technology, Transactions A: Science, 42(4), 2273-2288.
[2] Alizadeh, M., Cordeiro, G. M., Pinho, L. G. B., & Ghosh, I. (2017). The Gompertz-G Family of Distributions. Journal of Statistical Theory and Practice, 11 (1), 179-207.
[3] Al-Shomrani, A., Arif, O., Shawky, A., Hanif, S., & Shahbaz, M. Q. (2016). Topp-Leone Family of Distributions: Some Properties and Application. Pakistan Journal of Statistics and Operation Research, 12 (3), 443-451.
[4] Chambers, J., Cleveland, W., Kleiner, B., and Tukey, J. (1983). Graphical Methods for Data Analysis, Chapman and Hall, London.
[5] Chipepa, F., Makubate, B., Oluyede, B., & Rannona, K. (2021). The Topp Leone-G Power Series Class of Distributions with Applications. Pakistan Journal of Statistics and Operation Research, 17 (4), 827-846.
[6] Chipepa, F. and Oluyede, B. (2021). The Marshall-Olkin-Gompertz Fam- ily of Distributions: Properties and Applications. Journal of Non-linear Sciences and Applications, (14), 250-267.
[7] El-Bassiouny, A. H., Abdo, N. F., & Shahen, H. S. (2015). Exponential Lomax Distribution. International Journal of Computer Applications, 121 (13), 24-29.
[8] Jafari, A. A., & Tahmasebi, S. (2016). Gompertz-Power Series Distributions. Communications in Statistics-Theory and Methods, 45 (13), 3761- 3781.
[9] Johnson, N. L., Kotz, S., & Balakrishnan, N. (1994). Log-Normal Distributions. Continuous Univariate Distributions, 1, 207-27.
[10] Mahmoudi, E., & Jafari, A. A. (2012). Generalized Exponential–Power Series Distributions. Computational Statistics & Data Analysis, 56 (12), 4047-4066.
[11] Makubate, B., Gabanakgosi, M., Chipepa, F., & Oluyede, B. (2021). A new Lindley-Burr XII Power Series Distribution: Model, Properties and Applications. Heliyon, 7 (6), 1-11, e07146.
[12] Morais, A. L., & Barreto-Souza, W. (2011). A Compound Class of Weibull and Power Series Distributions. Computational Statistics & Data Analysis, 55 (3), 1410-1425.
[13] Oluyede, B., Chamunorwa, S., Chipepa, F. and Alizadeh, M. (2021). The Topp-Leone Gompertz-G Family of Distributions with Applications. Journal of Statistics & Management Systems, (In press).
[14] Oluyede, B., Chipepa, F., & Wanduku, D. (2021). The odd Weibull-Topp- Leone-G Power Series Family of Distributions: Model, Properties and Applications. Journal of Non-Linear Sciences and Applications, 14, 268- 286.
[15] Oluyede, B. O., Warahena-Liyanage, G., & Pararai, M. (2016). A New Compound Class of Log-Logistic Weibull–Poisson Distribution: Model, Properties and Applications. Journal of Statistical Computation and Simulation, 86 (7), 1363-1391.
[16] R´enyi, A. (1960). On Measures of Entropy and Information. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1, 547-561.
[17] Shams, S. & Alamatsaz, M. H. (2016). Generalized Linear Failure Rate Power Series Distribution. Communications in Statistics: Theory and Methods, 45 (8), 2204-2227.
[18] Silva, R. B., & Cordeiro, G. M. (2015). The Burr XII Power Series Distributions: A New Compounding Family. Brazilian Journal of Probability and Statistics, 29 (3), 565-589.
[19] Xu, K., Xie, M., Tang, L. C., & Ho, S. L. (2003). Application of Neural Networks in Forecasting Engine Systems Reliability. Applied Soft Computing, 2 (4), 255-268.