A NEW CUBIC TRANSMUTED LOG-LOGISTIC DISTRIBUTION: PROPERTIES, APPLICATIONS, AND CHARACTERIZATIONS
Keywords:
cubic transmutation, entropy, log-logistic distribution, maximum likelihood estimation, order statistics, reliability analysisDOI:
https://doi.org/10.17654/0972361724018Abstract
A new distribution, called the cubic transmuted log-logistic (CTLLog) distribution, is proposed. Various statistical properties of this distribution are presented. Expressions for the moments, quantile function, generating function, random number generation, reliability function, Shannon entropy, and order statistics with their moments are obtained for the proposed distribution. Certain characterizations of the CTLLog distribution are presented. The maximum likelihood estimation of the model parameters is done alongside a simulation study to investigate the performance of the estimation method. The applicability of this distribution is illustrated via a real-life data set.
Received: November 16, 2023
Accepted: January 4, 2024
References
A. Alzaatreh, C. Lee and F. Famoye, A new method for generating families of continuous distributions, Metron 71 (2013), 63-79.
G. R. Aryal, Transmuted log-logistic distribution, J. Stat. Appl. Pro. 2 (2013), 11 20.
A. Azzalini, A class of distributions that includes the normal ones, Scand. J. Statist. 12 (1985), 171-178.
G. M. Cordeiro and M. Castro, A new family of generalized distributions, J. Stat. Comput. Simul. 81 (2010), 883-898.
H. A. David and H. N. Nagaraja, Order Statistics, John Wiley Inc., USA, 2003.
N. Eugene, C. Lee and F. Famoye, Beta-normal distribution and its applications, Comm. Statist. Theory Methods 31 (2002), 497-512.
W. Glänzel, A characterization theorem based on truncated moments and its application to some distribution families, Math. Stat. Prob. Theory, Vol. B. Reidel, Dordrecht, 1987, pp. 75-84.
W. Glänzel, Some consequences of a characterization theorem based on truncated moments, Statistics 21 (1990), 613-618.
D. C. T. Granzotto and F. Louzada, The transmuted log-logistic distribution: modeling, inference, and an application to a polled Tabapua race time up to first calving data, Comm. Statist. Theory Methods 44 (2015), 3387-3402.
D. C. T. Granzotto, F. Louzada and N. Balakrishnan, Cubic rank transmuted distributions: inferential issues and applications, J. Stat. Comput. Simul. 87 (2017), 2760-2778.
M. M. Nassar and N. K. Nada, The beta generalized Pareto distribution, J. Stat.: Advan. Theory and App. 6 (2011), 1-17.
M. M. Rahman, B. Al-Zahrani and M. Q. Shahbaz, A general transmuted family of distributions, Pak. J. Stat. and Oper. Res. 14 (2018), 451-469.
M. M. Rahman, B. Al-Zahrani and M. Q. Shahbaz, Cubic transmuted Weibull distribution: properties and applications, Annals of Data Science 6 (2019), 83-102. doi:10.1007/s40745-018-00188-y
M. Q. Shahbaz, M. Ahsanullah, S. Hanif Shahbaz and B. Al-Zahrani, Ordered Random Variables: Theory and Applications, Atlantis Press and Springer, 2016.
C. E. Shannon, A mathematical theory of communication, The Bell System Technical Journal 27 (1948), 379-423.
W. T. Shaw and I. R. C. Buckley, The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-Kurtotic-normal distribution from a rank transmutation map, 2009. arXiv:0901.0434.
M. Zaindin and A. M. Sarhan, Parameters estimation of the modified Weibull distribution, Appl. Math. Sci. 3 (2009), 541-550.
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