Main Article Content
The problem of characterizing a probability distribution is an important problem which has attracted the attention of many researchers in the recent years. To understand the behavior of the data obtained through a given process, we need to be able to describe this behavior via its approximate probability law. This, however, requires to establish conditions which govern the required probability law. In other words we need to have certain conditions under which we may be able to recover the probability law of the data. So, characterization of a distribution plays an important role in applied sciences, where an investigator is vitally interested to find out if their model follows the selected distribution. In this short note, certain characterizations of three recently introduced discrete distributions are presented to complete, in some way, the works ofHussain(2020), Eliwa et al.(2020) and Hassan et al.(2020).
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- 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).
- Eliwa, M., Alhussain, Z., & El-Morshedy, M. (2020). Discrete Gompertz-G family of distributions for over-and under-dispersed data with properties, estimation, and applicationsMathematics, 8, 1-26. DOI: https://doi.org/10.3390/math8030358
- Galambos, J., & Kotz, S. (1978). Characterizations of probability distributions: A unified approach with an emphasis on exponential and related Models, Lecture Notes in Mathematics, Vol. 675. Springer.
- Glanzel, W. (1987). A characterization theorem based on truncated moments and its application to some distribution familiesMathematical Statistics and Probability Theory, B, 75–84. DOI: https://doi.org/10.1007/978-94-009-3965-3_8
- Glanzel, W., Teles, A., & Schubert, A. (1984). Characterization by truncated moments and its application to Pearson-type distributionsZeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 66(2), 173–182. DOI: https://doi.org/10.1007/BF00531527
- Glanzel, W., & Hamedani, G. (2001). Characterizations of the univariate continuous distributionsStudia Scientiarum Mathematicarum Hungarica, 37(1-2), 83–118. DOI: https://doi.org/10.1556/sscmath.37.2001.1-2.5
- Kim, J., & Jeon, Y. (2013). Credibility theory based on trimmingInsurance: Mathematics and Economics, 53(1), 36–47. DOI: https://doi.org/10.1016/j.insmatheco.2013.03.012
- Kotz, S., & Shanbhag, D. (1980). Some new approaches to probability distributionsAdvances in Applied Probability, 12(4), 903–921. DOI: https://doi.org/10.2307/1426748
- Hassan, A., Shalbaf, G., Bilal, S., & Rashid, A. (2020). A new flexible discrete distribution with applications to count dataJournal of Statistical Theory and Applications. DOI: https://doi.org/10.2991/jsta.d.200224.006
- Hussain, T. (2020). A zero truncated discrete distribution: Theory and applications to count dataPakistan Journal of Statistics and Operation Research, 16, 167-190. DOI: https://doi.org/10.18187/pjsor.v16i1.2133
- Nair, N., Sankaran, P., & Balakrishnan, N. (2018). Reliability modelling and analysis in discrete time. Academic Press.