Power unit Gumbel type II distribution: Statistical properties, regression analysis, and applications
Source abstract
Abstract
Using the power transformation method, we introduce a generalized version of the unit Gumbel type-2 distribution. The new lifetime distribution is called the power unit Gumbel type-2 distribution (PUGT2D). The new distribution’s statistical and reliability properties are given, and some estimation methods are proposed for estimating the model parameters. The usefulness and flexibility of the new distribution are illustrated with real datasets. Results based on log-likelihood, information statistics, and goodness-of-fit test results showed that the PUGT2D better fits the data than the other competing distributions. Moreover, a new regression model based on the new distribution is introduced and demonstrated to exhibit superior applicability through a numerical example.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Statistical Distribution Estimation and Applications · Probabilistic and Robust Engineering Design · Reliability and Maintenance Optimization
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Statistics and Operations Research, College of Science, King Saud University 1 , P.O. Box 2455, Riyadh 11451, Saudi Arabia
Department of Mathematics, Faculty of Science, Tanta University 2 , Tanta 31527, Egypt
3 Department of Mathematics, Amrita School of Physical Sciences, Coimbatore -641112, Amrita Vishwa Vidyapeetham, India
Department of Statistics, Faculty of Sciences, Selçuk University 4 , Konya, Türkiye
Department of Statistics, Faculty of Sciences, Selcuk University 5 , Konya, Türkiye
DICA, Politecnico di Milano, Piazza Leonardo da Vinci 32 6 , 20131 Milan (MI), Italy
Department of Mathematics, Pan-African Institute of Basic Science Technology and Innovation 7 , Nairobi, Kenya
Funding
King Saud University
References (28)
Show source-provided references
1. Systems of frequency curves generated by methods of translation10.1093/biomet/36.1-2.149 ↗
2. A generalized probability density function for double-bounded random processes10.1016/0022-1694(80)90036-0 ↗
3. Power lambert uniform distribution: Statistical properties, actuarial measures, regression analysis, and applications10.1063/5.0170964 ↗
4. Two-parameter family of distributions: Properties, estimation, and applications10.1063/5.0173532 ↗
5. Kotz · 200410.1017/CBO9780511550683 ↗
6. Power unit Burr-XII distribution: Statistical inference with applications10.1063/5.0171077 ↗
7. Estimating income inequality in China using grouped data and the generalized beta distribution10.1111/j.1475-4991.2007.00220.x ↗
8. A new 3-parameter bounded beta distribution: Properties, estimation, and applications10.3390/axioms11100504 ↗
9. The study of properties on generalized beta distribution10.1088/1742-6596/1132/1/012080 ↗
10. The unit-Weibull distribution and associated inference
11. The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval10.1080/03610926.2018.1476717 ↗
12. On the one parameter unit-Lindley distribution and its associated regression model for proportion data10.1080/02664763.2018.1511774 ↗
13. Unit Burr-III distribution with application10.1080/09720510.2019.1646503 ↗
14. The exponentiated Topp-Leone distribution: Properties and application
15. A bounded distribution derived from the shifted Gompertz law10.1016/j.jksus.2018.08.001 ↗
16. The log–Lindley distribution as an alternative to the beta regression model with applications in insurance10.1016/j.insmatheco.2013.10.017 ↗
17. Log-extended exponential–geometric distribution: Moments and inference based on generalized order statistics10.3390/sym15101857 ↗
18. A new heavy-tailed distribution defined on the bounded interval: The logit slash distribution and its application10.1080/02664763.2019.1704701 ↗
19. Beta regression for modelling rates and proportions10.1080/0266476042000214501 ↗
20. The Kumaraswamy distribution: Median-dispersion re-parameterizations for regression modeling and simulation-based estimation10.1007/s00362-011-0417-y ↗
21. A quantile regression model for bounded responses based on the exponential-geometric distribution10.57805/revstat.v18i4.309 ↗
22. The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates10.1080/02664763.2019.1657813 ↗
23. The unit log–log distribution: A new unit distribution with alternative quantile regression modeling and educational measurements applications10.1080/02664763.2021.2001442 ↗
24. A flexible probability model for proportion data: Unit Gumbel type-II distribution, development, properties, different method of estimations and applications10.17713/ajs.v52i2.1407 ↗
25. On the unit Burr-XII distribution with the quantile regression modeling and applications10.1007/s40314-021-01418-5 ↗
26. The unit Muth distribution: Statistical properties and applications10.1007/s11587-022-00703-7 ↗
27. Discrimination between the log-normal and the Weibull distributions10.1080/00401706.1973.10489124 ↗
28. Transmuted unit Rayleigh quantile regression model: Alternative to beta and Kumaraswamy quantile regression models