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Licensed Unlicensed Requires Authentication Published by De Gruyter June 19, 2018

Cubic Transmuted-G Family of Distributions and Its Properties

  • Muhammad Aslam EMAIL logo , Zawar Hussain ORCID logo and Zahid Asghar


In this article, a new family of distributions is introduced by using transmutation maps. The proposed family of distributions is expected to be useful in modeling real data sets. The genesis of the proposed family, including several statistical and reliability properties, is presented. Methods of estimation like maximum likelihood, least squares, weighted least squares, and maximum product spacing are discussed. Maximum likelihood estimation under censoring schemes is also considered. Further, we explore some special models of the proposed family of distributions and examined different properties of these special models. We compare three particular models of the proposed family with several existing distributions using different information criteria. It is observed that the proposed particular models perform better than different competing models. Applications of the particular models of the proposed family of distributions are finally presented to establish the applicability in real life situations.

MSC 2010: 46N30


[1] M. V. Aarset, How to identify bath tub hazard rate, IEEE Trans. Reliab. 36 (1987), 106–108. 10.1109/TR.1987.5222310Search in Google Scholar

[2] A. Afify, H. Yousof and S. Nadarajah, The beta transmuted-H family for lifetime data, Stat. Interface 10 (2017), no. 3, 505–520. 10.4310/SII.2017.v10.n3.a13Search in Google Scholar

[3] A. Z. Afify, M. Alizadeh, H. M. Yousof, G. Aryal and M. Ahmad, The transmuted geometric-G family of distributions: Theory and applications, Pakistan J. Statist. 32 (2016), no. 2, 139–160. Search in Google Scholar

[4] M. Alizadeh, F. Merovci and G. G. Hamedani, Generalized transmuted family of distributions: Properties and applications, Hacet. J. Math. Stat. 46 (2017), no. 4, 645–667. 10.15672/HJMS.201610915478Search in Google Scholar

[5] A. Alzaatreh, C. Lee and F. Famoye, A new method for generating families of continuous distributions, Metron 71 (2013), no. 1, 63–79. 10.1007/s40300-013-0007-ySearch in Google Scholar

[6] G. M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Stat. Comput. Simul. 81 (2011), no. 7, 883–898. 10.1080/00949650903530745Search in Google Scholar

[7] N. Eugene, C. Lee and F. Famoye, Beta-normal distribution and its applications, Comm. Statist. Theory Methods 31 (2002), no. 4, 497–512. 10.1081/STA-120003130Search in Google Scholar

[8] D. C. T. Granzotto, F. Louzada and N. Balakrishnan, Cubic rank transmuted distributions: Inferential issues and applications, J. Stat. Comput. Simul. 87 (2017), no. 14, 2760–2778. 10.1080/00949655.2017.1344239Search in Google Scholar

[9] F. Louzada and D. C. T. Granzotto, The transmuted log-logistic regression model: A new model for time up to first calving of cows, Statist. Papers 57 (2016), no. 3, 623–640. 10.1007/s00362-015-0671-5Search in Google Scholar

[10] A. Mahdavi and D. Kundu, A new method for generating distributions with an application to exponential distribution, Comm. Statist. Theory Methods 46 (2017), no. 13, 6543–6557. 10.1080/03610926.2015.1130839Search in Google Scholar

[11] P. R. D. Marinho, G. M. Cordeiro, F. Peña Ramírez, M. Alizadeh and M. Bourguignon, The exponentiated logarithmic generated family of distributions and the evaluation of the confidence intervals by percentile bootstrap, Braz. J. Probab. Stat. 32 (2018), no. 2, 281–308. 10.1214/16-BJPS343Search in Google Scholar

[12] A. W. Marshall and I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika 84 (1997), no. 3, 641–652. 10.1093/biomet/84.3.641Search in Google Scholar

[13] 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, Research report, Department of Mathematics, King’s College London, 2007. Search in Google Scholar

[14] K. Zografos and N. Balakrishnan, On families of beta- and generalized gamma-generated distributions and associated inference, Stat. Methodol. 6 (2009), no. 4, 344–362. 10.1016/j.stamet.2008.12.003Search in Google Scholar

Received: 2017-11-04
Revised: 2018-05-21
Accepted: 2018-05-21
Published Online: 2018-06-19
Published in Print: 2018-12-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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