Discrete Exponentiated Generalized Family of Distributions | ||||
Computational Journal of Mathematical and Statistical Sciences | ||||
Volume 2, Issue 2, November 2023, Page 303-327 PDF (652.45 K) | ||||
Document Type: Original Article | ||||
DOI: 10.21608/cjmss.2023.240287.1020 | ||||
View on SCiNiTO | ||||
Authors | ||||
Abeer E. Abd EL-Hady1; Mai A. Hegazy 1; Abeer A. EL-Helbawy 2 | ||||
1Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls' Branch), Tafahna Al-Ashraf, Egypt | ||||
2Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls' Branch), Cairo, Egypt | ||||
Abstract | ||||
In this paper, exponentiated-G family of distributions is constructed as a new family of discrete distribution, using the general approach of discretization of a continuous distribution. Some statistical properties including quantiles, mean residual life, mean time to failure, mean time between failure, availability, Re ́nyi entropy, moments and order statistics are obtained. Discrete exponentiated inverted Topp–Leone distribution as a member of this family is studied in detail. Maximum likelihood approach is applied under Type-II censored sample for estimating the unknown parameters of the exponentiated inverted Topp–Leone distribution. Also, maximum likelihood estimators of the survival, hazard rate and alternative hazard rate functions are derived. The confidence intervals for the parameters, survival, hazard rate and alternative hazard rate functions are obtained. A simulation study is performed to investigate the accuracy of the theoretical results. Finally, two real data sets are analyzed to illustrate the flexibility and applicability of the proposed model for real-life applications. | ||||
Keywords | ||||
Survival discretization; Exponentiated-G family; Order statistic; Maximum likelihood | ||||
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