Main Article Content
Abstract
In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass function and an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distribution including the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and L- moment statistics have been established. Two actuarial or risk measures were derived. The numerical computations for these measures are conducted for several parametric values of the model parameter. The parameter of the introduced distribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conducted to explore the performance of the studied estimators. The performance of the proposed distribution has been examined by three over-dispersed real data sets from biological sciences.
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
-
1. Al-Babtain, A. A., Ahmed, A. H. N. and Afify, A. Z. (2020). A new discrete analog of the continuous Lindley
distribution, with reliability applications. Entropy, 22, 603.
2. Almazah, M. M. A., Erbayram, T., Akdo˘gan, Y., AL Sobhi, M. M. and Afify, A.Z. (2021). A new extended
geometric distribution: properties, regression model, and actuarial applications. Mathematics, 9, p.1336. 3.
Artzner, P. (1999). Application of coherent risk measures to capital requirements in insurance. N. Am. Actuar.
J., 3, 11-25.
4. Eliwa, M. S., Alhussain, Z. A., El-Morshedy, M. (2020a). Discrete Gompertz-G family of distributions
for over- and under-dispersed data with properties, estimation and applications. Mathematics, 8, 358,
doi:10.3390/math8030358.
5. Eliwa, M. S., Altun, E., El-Dawoody, M. and El-Morshedy, M. (2020b). A new three-parameter discrete
distribution with associated INAR (1) process and applications. IEEE access, 8, 91150-91162.
6. Eliwa, M. S., El-Morshedy, M. and Altun, E. (2020c). A study on discrete Bilal distribution with properties
and applications on integer-valued autoregressive process. Revstat statistical journal. Forthcoming.
7. El-Morshedy, M., Eliwa, M. S. and Altun, E. (2020a). Discrete Burr-Hatke distribution with properties,
estimation methods and regression model. IEEE access, 8, 74359-74370..
8. El-Morshedy, M., Eliwa, M. S. and Nagy, H. (2020b). A new two-parameter exponentiated discrete Lindley
distribution: properties, estimation and applications. Journal of applied statistics, 47, 354-375.
9. Feigl, P. and Zelen, M. (1965). Estimation of exponential probabilities with concomitant information.
Biometrics, 21, 826–838.
10. G´omez-D´eniz, E. (2010). Another generalization of the geometric distribution. Test, 19, 399–415.
11. Gupta, P. L., Gupta, R. C., and Tripathi, R. C. (1997). On the monotonic properties of discrete failure rates.
Journal of statistical planning and inference, 65, 255-268.
12. Jazi, M. A., Lai, C. D., Alamatsaz, M. H. (2010). A discrete inverse Weibull distribution and estimation of
its parameters. Stat. Methodol., 7, 121-132.
13. Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012). Loss Models: From Data to Decisions. John
Wiley & Sons: Hoboken, NJ, USA, Volume 715.
14. Krishna, H. and Pundir, P. S. (2009) Discrete Burr and discrete Pareto distributions. Stat. Methodol., 6,
177-188.
15. Ramos, P. L. and Louzada, F. (2019). A distribution for instantaneous failures. Stats, 2, 247-258.