Exponentiated uniform distribution: An interesting alternative to truncated models
DOI:
https://doi.org/10.5433/1679-0375.2019v40n2p107Keywords:
Limited Support Distributions, Maximum Likelihood Estimation, Exponentiated distributionsAbstract
In this paper some properties of the so-called exponentiated uniform distribution are derived and discussed, such as quantile function, moments, generating function, mean deviations, Bonferroni and Lorenz curves, Shannon and Rényi entropies. The proposed model, defined in the range [a;b] can be used as an alternative to the truncated models. The maximum likelihood estimation of the model parameter is also conducted and a simulation study was performed to verify the consistency of model parameter. An application to a real data set illustrates its potentiality comparing the new distribution with other three well-known truncated distributions.We also present, at the end, an section discussing about computational codes, where the scripts used in R software are available.Metrics
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References
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BOURGUIGNON, M.; SILVA, R. B.; CORDEIRO, G. M. The Weibull-G Family of Probability Distributions. Journal of Data Science, New York, v. 12, p. 53–68, 2014.
CORDEIRO, G. M.; ORTEGA, E. M. M.; CUNHA, D. C. C. The Exponentiated Generalized Class of Distributions. Journal of Data Science, New York, v. 11, p. 1–27, 2013.
GUPTA, R. C.; GUPTA, P. L.; GUPTA, R. D. Modeling failure time data by Lehman alternatives. Communications in Statistics, Theory and Methods, New York, v. 27, p. 887– 904, 1998.
GUPTA, R. D.; KUNDU, D. Exponentiated exponential family: an alternative to Gamma andWeibull distributions. Biometrical Journal, Weinheim, v. 43, p. 117–130, 2001.
LEE, C.; WON, H.Y. Inference on reliability in an exponentiated uniform distribution. Journal of the Korean Data & Information Science Society, Gyeongsan-si, v. 17, p. 507–513, 2006.
NADARAJAH, S.; KOTZ, S. The exponentiated type distributions. Acta Applicandae Mathematicae, Heidelberg, v. 92, p. 97–111, 2006b.
PESCIM, R. R.; CORDEIRO, G. M.; DEMÉTRIO, C. G. B.; ORTEGA, E. M. M.; NADARAJAH, S. The newclass of Kummer beta generalized distributions. SORT, Barcelona, v. 36, p. 153–180 2012.
RÉNYI, A. On the measures of entropy and information. Proceedings of Fourth Berkeley Symposium on Mathematics, Statistics and Probability, Berkeley, v. 1, p. 547–561, 1961.
RISTIC, M. M.; BALAKRISHNAN, N. The gamma exponentiated exponential distribution. Journal of Statistical Computation and Simulation, Philadelphia, v. 82, p. 1191– 1206, 2012.
SHANNON, C. E. Prediction and Entropy of Printed English. Bell System Technical Journal, New York, v. 30, p. 50–64, 1951.
STASINOPOULOS, M.; RIGBY, B. gamlss. tr: Generating and Fitting Truncated gamlss.family Distributions. 2016. Available: <https://CRAN.R-project.org/package= gamlss.tr.> Access in: 01/05/2019.
TORABI, H.; MONTAZERI, N.H. The Logistic-Uniform distribution and its applications. Communications in Statistics - Simulation and Computation, New York, v. 43, p. 2551–2569, 2014.
TORABI, H.; MONTAZERI, N.H. The Gamma-Uniform distribution and its applications. Kybernetika, Prague, v. 48, p. 16–30, 2012.
ZOGRAFOS, K.; BALAKRISHNAN, N. On families of beta– and generalized gamma–generated distributions and associated inference. Statistical Methodology, Amsterdam, v. 6, p. 344–362, 2009.
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Published
2019-12-18
How to Cite
Ramires, T. G., Nakamura, L. R., Righetto, A. J., Pescim, R. R., & Telles, T. S. (2019). Exponentiated uniform distribution: An interesting alternative to truncated models. Semina: Ciências Exatas E Tecnológicas, 40(2), 107–114. https://doi.org/10.5433/1679-0375.2019v40n2p107
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