The Type II Exponentiated Half Logistic-Gompertz-G Power Series Class of Distributions: Properties and Applications
Abstract
We propose and study a new generalized class of distributions called the Type II Exponentiated Half Logistic-Gompertz-G Power Series (TIIEHL-Gom-GPS) distribution. Some structural properties including expansion of density,ordinary and conditional moments, generating function, order statistics and entropy are derived. We present some specialcases of the proposed distribution. The maximum likelihood method is used for estimating the model parameters. Theimportance of the new class of distributions are illustrated by means of two applications to real data sets.References
Alizadeh, M., Cordeiro, G. M., Pinho, L. G. B. and Ghosh, I., The Gompertz-G family of distributions, Journal of Statistical Theory and Practice, vol. 11, no. 1, pp. 179-207, 2017.
Alizadeh, M., Rasekhi , M., Yousof, H. M., Hamedani, G., and Ataei, A., The Odd Log-Logistic Transmuted-G family of distributions: properties, characterization, applications and different methods of estimation, Statistics, Optimization & Information Computing, vol. 10, no. 3, pp. 904-924, 2022.
Al-Mofleh, H., Elgarhy, M., Afify, A., and Zannon, M., Type II exponentiated half logistic generated family of distributions with applications, Electronic Journal of Applied Statistical Analysis, vol. 13, no. 2, pp. 536-561, 2020.
Bantan, R.A., Jamal, F., Chesneau, C., and Elgarhy M., Type II power Topp-Leone generated family of distributions with statistical inference and applications, Symmetry, vol. 12, no. 1, pp. 75, 2020.
Bjerkedal, T., Acquisition of resistance in Guinea pigs infected with different doses of virulent tubercle bacilli, American Journal of Hygiene, vol. 72, pp. 130-148, 1960.
Chambers, J., Cleveland, W., Kleiner, B. and Tukey, P., Graphical methods of data analysis, Chapman and Hall, 1983.
Chen, G. and Balakrishnan, N., A general purpose approximate goodness-of-fit test, Journal of Quality Technology, vol. 27, no. 2, pp. 154-161, 1995.
Chipepa, F., Oluyede, B. and Wanduku, D., The exponentiated half logistic odd Weibull-Topp-Leone-G: Model, properties and applications, Journal of Statistical Modeling: Theory and Applications, vol. 2, no. 1, pp. 15-38, 2021.
Chipepa, F., Oluyede, B., Makubate, B., & Fagbamigbe A., F., The beta odd Lindley-G family of distributions with applications Journal of Probability and Statistical Science, vol. 17, no. 1, pp. 51-83, 2019.
Chipepa, F., Oluyede, B. and Makubate, B., The odd generalized half-logistic Weibull-G family of distributions: properties and applications, Journal of Statistical Modeling: Theory and Applications, vol. 11, no. 1, pp. 65-89, 2020.
Chipepa, F. and Oluyede, B., The Marshall-Olkin-Gompertz-G family of distributions: properties and applications, Journal of Nonlinear Sciences and Applications, vol. 14, no. 4, pp. 250-267, 2021.
Cordeiro, G. M. Ortega, E. M. M. and Nadarajaah, S., The Kumaraswamy Weibull distribution with application to failure data, Journal of the Franklin Institute, pp. 1399 -1429, 2010.
Goldoust, M., Mohammadpour, A., Alizadeh, M., and Hamedani, G., A new generalized family of lifetime distributions motivated by parallel and series structures, Statistics, Optimization & Information Computing, vol. 7, no. 4, pp. 779-801, 2019.
Gradshetyn, I. S., and Ryzhik, I. M., Tables of integrals, series and products, Sixth Edition, Academic Press, San Diego, 2000.
Kharazmi, O., Paghale, F. J., Nik, A. S., Dey, S., and Alizadeh , M., A New Two-Sided Class of Lifetime Distributions: Applications to Complete and Right Censored Data, Statistics, Optimization & Information Computing, vol. 11, no. 3, pp. 595-614, 2023.
Makubate, B., Chamunorwa, S., Oluyede, B. and Chipepa, F., The Marshall-Olkin-Odd Weibull-G family of distributions: model, properties and applications, Eurasian Bulletin of Mathematics, vol. 4, no. 2, pp. 71-97, 2021.
Moakofi, T., Oluyede, B., and Chipepa, F., Type II Exponentiated Half-Logistic-Topp-Leone-G power series class of distributions with applications, Pakistan Journal of Statistics and Operation Research, vol. 17, no. 4, pp. 885-909, 2021.
Oluyede, B., Chipepa, F. and Wanduku, D., The odd Weibull-Topp-Leone-G power series family of distributions model, properties, and applications, Journal of Nonlinear Science and Application, vol. 14, pp. 60-65, 2021.
Oluyede, B., Chamunorwa, S., Chipepa, F., and Alizadeh, M., The Topp-Leone-Gompertz-G family of distributions with applications Journal of Statistics and Management Systems, vol. 25, no. 6, pp 1399-1423, 2022.
R´enyi, A., On measures of entropy and information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 547–561, 1960.
Sanku, D., Fernando, A. M. and Devendra, K., Statistical properties and different methods of estimation of Gompertz distribution with application, Journal of Statistics and Management Systems, vol. 21, no. 5, pp. 839-876, 2018.
Soliman, A.H., Elgarhy, M.A.E., and Shakil, M., Type II half logistic family of distributions with applications. Pakistan Journal of Statistics and Operations Research, pp 245-264, 2017.
Shannon, C. E., Prediction and entropy of printed english, The Bell System Technical Journal, vol. 30, pp. 50-64, 1951.
ZeinEldin, R.A., Hashmi, S., Elsehety, M., and Elgarhy, M., Type II half-logistic Kumaraswamy distribution with applications, Journal Function Spaces, 2020.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
