Document Type
Article
Publication Date
2021
Publisher
Università di Bologna Dipartimento di Scienze Statistiche
Source Publication
Statistica
Source ISSN
0390-590x
Abstract
In this work, a new discrete distribution which includes the discrete Burr-Hatke distribution is defined and studied. Relevant statistical properties are derived. The probability mass function of the new distribution can be "right skewed" with different shapes, bimodal and "uniformed". Also, the corresponding hazard rate function can be "monotonically decreasing", "upside down", "monotonically increasing", "upside down increasing", and "upside down-constant-increasing". A numerical analysis for the mean, variance, skewness, kurtosis and the index of dispersion is presented. The new distribution could be useful in the modeling of "under-dispersed" or "overdispersed" count data. Certain characterizations of the new distribution are presented. These characterizations are based on the conditional expectation of a certain function of the random variable and in terms of the hazard rate function. Bayesian and non-Bayesian estimation methods are considered. Numerical simulations for comparing Bayesian and non-Bayesian estimation methods are performed. The new model is applied for modeling carious teeth data and counts of cysts of kidneys data.
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Recommended Citation
Yousof, Haitham M.; Chesneau, Christophe; Hamedani, Gholamhossein; and Ibrahim, Mohamed, "A New Discrete Distribution: Properties, Characterizations, Modeling Real Count Data, Bayesian and Non-Bayesian Estimations" (2021). Mathematical and Statistical Science Faculty Research and Publications. 78.
https://epublications.marquette.edu/math_fac/78
Comments
Published version. Statistica, Vol. 81, No. 2 (2021): 135-162. DOI. © 2021 Università di Bologna Dipartimento di Scienze Statistiche.