Discrete Logistic Exponential Distribution with Application
Abstract
In this paper, a new two-parameter discrete logistic exponential distribution is proposed based on the survival discretization approach. Some statistical properties are derived, and it is found that the proposed model can be used to discuss several kinds of failure rates including unimodal, bathtub, and increasing-shaped. Moreover, it can be utilized effectively to model under- and over-dispersed data. The distribution parameters are estimated using the maximum likelihood technique. The behavior of maximum likelihood estimators is assessed utilizing a comprehensive simulation study. In the end, two real data are analyzed to show the usefulness of the new discrete distribution.References
A. AL-Huniti, A., & R. AL-Dayian, G. (2012). Discrete Burr Type Iii Distribution. American Journal of Mathematics and Statistics, 2(5), 145–152. https://doi.org/10.5923/j.ajms.20120205.07
Ahsan-ul-Haq, M., Babar, A., Hashmi, S., Alghamdi, A. S., & Afify, A. Z. (2021). The Discrete Type-II Half-Logistic Exponential Distribution with Applications to COVID-19 Data. Pakistan Journal of Statistics and Operation Research, 921–932.
Al-dayian, G. R. (2019). Bayesian Estimation and Prediction of Discrete Gompertz Distribution Bayesian Estimation and Prediction of Discrete Gompertz Distribution. 36(May), 1–21. https://doi.org/10.9734/JAMCS/2021/v36i230335
Alamatsaz, M. H., Dey, S., Dey, T., & Harandi, S. S. (2016). DISCRETE GENERALIZED RAYLEIGH DISTRIBUTION. Pakistan
Journal of Statistics, 32(1).
Alghamdi, A. S., Ahsan-ul-Haq, M., Babar, A., Aljohani, H. M., Afify, A. Z., & Cell, Q. E. (2022). The discrete power-Ailamujia distribution: properties, inference, and applications. AIMS Mathematics, 7(5), 8344–8360.
Ali, S., Dey, S., Tahir, M. H., & Mansoor, M. (2020). Two-Parameter Logistic-Exponential Distribution: Some New
Properties and Estimation Methods. American Journal of Mathematical and Management Sciences, 39(3), 270–298.
https://doi.org/10.1080/01966324.2020.1728453
Almetwally, E. M., & Gamal, M. I. (2020). Discrete Alpha Power Inverse Lomax Distribution with Application of COVID-19 Data. International Journal of Applied Mathematics, 9(6), 11–22.
Bodhisuwan, W., & Sangpoom, S. (2017). The discrete weighted Lindley distribution. Proceedings - 2016 12th International Conference on Mathematics, Statistics, and Their Applications, ICMSA 2016: In Conjunction with the 6th Annual International Conference of Syiah Kuala University, 99–103. https://doi.org/10.1109/ICMSA.2016.7954317
Chan, S. K., Riley, P. R., Price, K. L., McElduff, F., Winyard, P. J., Welham, S. J., ... & Long, D. A. (2010). Corticosteroid-induced kidney dysmorphogenesis is associated with deregulated expression of known cystogenic molecules, as well as Indian hedgehog. American journal of physiology-renal physiology, 298(2), F346-F356.
Eldeeb, A. S., Ahsan-Ul-Haq, M., & Babar, A. (2021). A Discrete Analog of Inverted Topp-Leone Distribution: Properties, Estimation and Applications. International Journal of Analysis and Applications, 19(5), 695–708.
Eldeeb, A. S., Ahsan-ul-Haq, M., & Eliwa, M. S. (2021). A discrete Ramos-Louzada distribution for asymmetric and over-dispersed data with leptokurtic-shaped: Properties and various estimation techniques with inference. AIMS Mathematics, 7(2), 1726–1741. https://doi.org/10.3934/math.2022099
Eliwa, M. S., Altun, E., El-Dawoody, M., & El-Morshedy, M. (2020). A new three-parameter discrete distribution with associated INAR (1) process and applications. IEEE access, 8, 91150-91162.
Eliwa, M. S., & El-Morshedy, M. (2022). A one-parameter discrete distribution for over-dispersed data: Statistical and reliability properties with applications. Journal of Applied Statistics, 49(10), 2467-2487. https://doi.org/10.1080/02664763.2021.1905787
El-Morshedy, M., Eliwa, M. S., & Altun, E. (2020). Discrete Burr-Hatke distribution with properties, estimation methods and regression model. IEEE access, 8, 74359-74370.
El-Morshedy, M., Eliwa, M. S., & Nagy, H. (2020). A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications. Journal of applied statistics, 47(2), 354-375. https://doi.org/10.1080/02664763.2019.1638893
Gleaton, J. U., & Lynch, J. D. (2006). Properties of generalized log-logistic families of lifetime distributions. Journal of Probability and Statistical Science, 4(1), 51–64.
G´omez-D´eniz, E., & Calder´ın-Ojeda, E. (2011). The discrete Lindley distribution: properties and applications. Journal of Statistical Computation and Simulation, 81(11), 1405–1416.
Krishna, H., & Pundir, P. S. (2009). Discrete Burr and discrete Pareto distributions. Statistical Methodology, 6(2), 177–188.
Lan, Y., & Leemis, L. M. (2008). The logistic–exponential survival distribution. Naval Research Logistics (NRL), 55(3), 252–264.
Nakagawa, T., & Osaki, S. (1975). The discrete Weibull distribution. IEEE Transactions on Reliability, 24(5), 300–301.
Para, B. (2016). Discrete Version of Log-Logistic Distribution and Its Applications in Genetics. International Journal of Modern Mathematical Sciences, (November). Retrieved from http://www.modernscientificpress.com
Para, B. A. (2014). Discrete Generalized Burr-Type XII Distribution Discrete Generalized Burr-Type XII. 13(2).
Para, B. A., & Jan, T. R. (2017). Discrete Inverse Weibull Minimax Distribution: Properties and Applications. Journal of Statistics Applications & Probability, 218(1), 205–218. Retrieved from http://dx.doi.org/10.18576/jsap/060116
Roy, D. (2004). Discrete rayleigh distribution. IEEE Transactions on Reliability, 53(2), 255–260.
- 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).
