New odd Chen Fréchet distributions: Properties and applications

Document Type : Research Paper


Department of Statistics, College of Administration and Economics, Karbala University, Iraq


To introduce a new four-parameter lifetime distribution that will be more flexible in modelling real lifetime data over the existing common lifetime distributions. The new four-parameter lifetime distribution is generated by using the odd Chen generator of distributions. In this method, the probability density function and cumulative distribution function of Fréchet distributions are used as a base distribution for odd Chen Fréchet distributions. The probability density function and cumulative distribution function of the Fréchet distributions are substituted in the odd Chen generator of the distributions model to get the new and more flexible lifetime distribution for modelling real-life data. The authors reveal that the hazard rate of the odd Chen Fréchet distributions is increasing. They also found that the odd Chen generator of distributions gives a much close fit than the Fréchet Distribution (FD), Weibull distribution(WD), and exponential distribution (ED).  In this study, a novel probability distribution is introduced. odd Chen generator of distributions is capable of modelling upside-down bathtub-shaped hazard rates. The model is appropriate to fit the asymmetrical data that are not correctly fitted by other distributions. The said distribution can be applied to different fields like insurance, earthquake data for analysis, reliability etc.


[1] A.Z. Afify, G. Hamedani, I. Ghosh, and M.E. Mead, The transmuted Marshall-Olkin Fr´echet distribution: Properties and applications, Int. J. Statist. Probab. 4 (2015), no. 4, 132–148.
[2] A.Z. Afify, H.M. Yousof, G.M. Cordeiro, E.M. M. Ortega, and Z.M. Nofal, The Weibull Fr´echet distribution and its applications, J. Appl. Statist. 43 (2016), no. 14, 2608–2626.
[3] A.Z. Afify, H.M. Yousof, G.M. Cordeiro, Z.M. Nofal, and A.N. Ahmed, The Kumaraswamy Marshall-Olkin Fr´echet distribution with applications, J. ISOSS 2 (2016), no. 2, 151–168.
[4] W. Barreto-Souza, G.M. Cordeiro, and A.B. Simas, Some results for beta fr´echet distribution, Commun. Statist. Theory Meth. 40 (2011), 798–811.
[5] R.V. da Silva, T.A.N. de Andrade, D.B.M. Maciel, R.P.S. Campos, and G.M. Cordeiro, A new lifetime model: The gamma extended Fr´echet distribution, J. Stat. Theory Appl. 12 (2016), no. 1, 39–54.
[6] S. Kotz and S. Nadarajah, Extreme value distributions: theory and applications, World Scientific, 2000.
[7] E. Krishna, K.K. Jose, T. Alice, and M.M. Risti´c, The Marshall-Olkin Fr´echet distribution, Commun. Statist. Theory Meth. 42, no. 22, 4091–4107.
[8] M.R. Mahmoud and R.M. Mandouh, On the transmuted Fr´echet distribution, J. Appl. Sci. Res. 9 (2013), no. 10, 5553–5561.
[9] M.E. Mead, A.Z. Afify, G.G. Hamedani, and I. Ghosh, The beta exponential Fr´echet distribution with applications, Austr. J. Statist. 46 (2017), no. 1, 41–63.
[10] M.E.A. Mead, A note on Kumaraswamy Fr´echet distribution, Austr. J. Basic Appl. Sci. 8 (2014), 294–300.
[11] S. Nadarajah and A.K. Gupta, The beta Fr´echet distribution, Fareast J. Theor. Statist. 14 (2004), no. 1, 15–24.
[12] S. Nadarajah and S. Kotz, The exponentiated Fr´echet distribution, Interstat Electronic J. 14 (2003), 1–7.
[13] H.M. Yousof, A.Z. Afify, N.E. Abd El Hadi, G.G. Hamedani, and N.S. Butt, On six-parameter Fr´echet distribution: properties and applications, Pakistan J. Statist. Oper. Res. 12 (2016), no. 2, 281–299.
Volume 14, Issue 4
April 2023
Pages 151-160
  • Receive Date: 10 December 2022
  • Revise Date: 10 January 2023
  • Accept Date: 02 February 2023
  • First Publish Date: 03 February 2023