DOI QR코드

DOI QR Code

ON THE CLASS OF TRANSMUTED-G DISTRIBUTIONS

  • Received : 2021.08.29
  • Accepted : 2022.03.19
  • Published : 2022.09.30

Abstract

In this article, we compare the reliability and the hazard function between a baseline distribution and the corresponding transmuted-G distribution. Some examples based on existing transmuted-G distributions in literature are used. Three tests of parameter significance are utilized to test the importance of a transmuted-G distribution over the baseline distribution, and real data is used in an application of the inference about the importance of transmuted-G distributions.

Keywords

Acknowledgement

The work of the first author was supported by the Deanship of Scientific Research at the University of Jordan.

References

  1. A. Alzaatreh, C. Lee, and F. Famoye, A new method for generating families of continuous distributions, Metron 71 (2013), 63-79. https://doi.org/10.1007/s40300-013-0007-y
  2. M.A. Aljarrah, C. Lee, and F. Famoye, On generating T-X family of distributions using quantile functions, J. Stat. Dist. and Applications 1 (2014), 1-17. https://doi.org/10.1186/2195-5832-1-1
  3. D.F. Andrews and A.M. Herzberg, Data: A Collection of Problems from Many Fields for the Student and Research Worker, Springer Series in Statistics, New York, 1985.
  4. G.R. Aryal and C.P. Tsokos, Transmuted Weibull distribution: A Generalization of the Weibull Probability Distribution, Eur. J. Pure App. Mathematics 4 (2011), 89-102.
  5. R.E. Barlow, R.H. Toland, and T. Freeman, A Bayesian analysis of stress-rupture life of Kevlar 49/epoxy spherical pressure vessels, Proc. Canad. Conf. App. Statistics, Marcel Dekker, New York, 1984.
  6. M. Bourguignon, I. Ghosh, and G. Cordeiro, General results for the transmuted family of distributions and new models, Journal of Probability and Statistics 2016 (2016), Article ID 7208425. http://dx.doi.org/10.1155/2016/7208425
  7. F. Merovci, Transmuted Rayleigh distribution, Aus. J. of Statistics 42 (2013), 21-31. https://doi.org/10.17713/ajs.v42i1.163
  8. F. Merovci, M. Alizadeh, and G.G. Hamedani, Another generalized transmuted family of distributions: properties and applications, Aus. J. of Statistics 45 (2016), 71-93.
  9. J. Neyman, and E.S. Pearson, On the use and interpretation of certain test criteria for purposes of statistical inference, Biometrika 20 (1928), 175-240.
  10. Z.M. Nofal, A.Z. Afify, H.M. Yousof, and F. Louzada, The transmuted exponentiated additive Weibull distribution: properties and applications, J. Mod. App. Statistical Methods 17 (2018), eP2526. doi: 10.22237/jmasm/1525133340
  11. C.R. Rao, Large sample tests of statistical hypotheses concerning several parameters with application to problems of estimation, Proc. Camb. Philosophical Society 44 (1948), 50-57. https://doi.org/10.1017/S0305004100023987
  12. W.T. Shaw and I.R.C. Buckley, The Alchemy of Probability Distributions: Beyond GramCharlier & Cornish-Fisher Expansions, and Skew-Normal or Kurtotic-Normal Distributions, Research report at the Austrian School of Statistics, 2007.
  13. A. Wald, Tests of statistical hypotheses concerning several parameters when the number of observations is large, Transactions of the American Mathematical Society 54 (1943), 426-482. https://doi.org/10.1090/S0002-9947-1943-0012401-3