The Rayleigh Gompertz distribution: Theory and real applications

Document Type : Research Paper


1 Mathematics Department, College of Science, Mustansiriyah University, Baghdad, Iraq

2 Mathematics Department, College of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq


The generalization of distributions is an important topic in probability theory. Several distributions, whether symmetrical, semi-symmetrical or heavily skewed, are unsuitable for modelling modern data. In this paper, the Rayleigh Gompertz distribution as a new compound flexible distribution is introduced. Several important statistical properties of the new distribution have been examined and studied as well as its flexibility is proved through various real datasets with different information fitting criteria. The flexibility of this new distribution allows using it in various application areas.


[1] N. Eugene, C. Lee and F. Famoye, Beta-normal distribution and its applications, Commun. Statist.- Theory Meth.
31(4) (2002) 497–512.
[2] 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(5) (1997) 641–652.
[3] K. Zografos and N. Balakrishnan, On families of beta and generalized gamma-generated distributions and associated inference, Statist. Meth. 6(4) (2009) 344–362.
[4] G.M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Stat. Comput. Simul. 81(7) (2011)
[5] M. Bourguignon, R.B. Silva and G.M. Cordeiro, The Weibull-G family of probability distributions, J. Data Sci.
12(1)(2014) 53–68.
[6] N.H. Al-Noor and N. K. Assi, Rayleigh-Rayleigh distribution: properties and applications, J. Phys. Conf. Ser.
1591 (2020) 012038.
[7] T.I. Missov and A. Lenart, Linking period and cohort life-expectancy linear increases in Gompertz proportional
hazards models, Demographic Res. 24 (2011) 455–468.
[8] J.H. Pollard and E.J. Valkovics, The Gompertz distribution and its applications, Genus. 48(3)(1992) 15–28.
[9] A.A. Jafari, S. Tahmasebi and M. Alizadeh, The beta-Gompertz distribution, Rev. Colomb. de Estad´─▒st. 37
(1)(2014) 139–156.
[10] N.H. Al-Noor and N.K. Assi, Rayleigh Gamma Gompertz distribution: properties and applications, AIP Conf.
Proc. 2334(1)(2021) 090003.
[11] A. El-Gohary, A. Alshamrani and A.N. Al-Otaibi, The generalized Gompertz distribution, Appl. Math. Modell.
37(1-2) (2013) 13-24.
[12] B.M. Mathers, L. Degenhardt, C. Bucello, J. Lemon, L. Wiessing and M. Hickman, Mortality among people who
inject drugs: a systematic review and meta-analysis, Bull. World Health Organ. 91(2) (2013) 102–123.
[13] P. Nasiri and H. Pazira, Bayesian approach on the generalized exponential distribution in the presence of outliers,
J. Statist. Theory Pract. 4(3) (2010) 453–475.
[14] H.A. Schafft, T.C. Staton, J. Mandel and J.D. Shott, Reproducibility of electromigration measurements, IEEE
Trans. Electron. Devices 34(3) (1987) 673–681.
[15] D. Kundu and M.Z. Raqab, Estimation of R = P(X < Y ) for three parameter Weibull distribution, Stat. Probab.
Lett. 79(17) (2009) 1839–1846.
[16] M.E. Ghitany, R.A. Al-Jarallah and N. Balakrishnan, On the existence and uniqueness of the MLEs of the
parameters of a general class of exponentiated distributions, Statist. 47(3) (2013) 605–612.
[17] T.I. Missov, Gamma-Gompertz life expectancy at birth, Demographic Res. 28 (2013) 259–270.
[18] S. Yaghoobzadeh, A new generalization of the Marshall–Olkin Gompertz distribution, Int. J. Syst. Assur. Eng.
Manage. 8 (2017) 1580–1587.
[19] R.C. da Silva, J.J.D. Sanchez, F.P. Lima and G.M. Cordeiro, The Kumaraswamy Gompertz distribution, J. Data
Sci. 13(2015) 241–260.
[20] M.M.M. El-Din, Y. Abdel-Aty and M.H. Abu-Moussa, Statistical inference for the Gompertz distribution based
on type-ii progressively hybrid censored data, Commun. Stat.- Simul. Comput. 46(8) (2017) 6242–6260.
[21] O.A. Ade, Performance rating of the exponentiated generalized Gompertz Makeham distribution: An analytical
approach, Am. J. Theor. Appl. Statist. 6(5) (2017) 228–235.
Volume 13, Issue 1
March 2022
Pages 3505-3516
  • Receive Date: 11 March 2021
  • Revise Date: 12 May 2021
  • Accept Date: 29 June 2021