Parameter estimation of inverse exponential Rayleigh distribution based on classical methods

Document Type : Research Paper


Department of mathematics, College Of Education For Pure Sciences (Ibn AL-Haitham), University of Baghdad, Iraq


This paper introduces and developed a new lifetime distribution known as inverse exponential Rayleigh distribution (IERD). The new two-scale parameters generalized distribution was studies with its distribution and density functions, besides that the basic properties such as survival, hazard, cumulative hazard, quantile function, skewness, and Kurtosis functions were established and derived. To estimate the model parameters, maximum likelihood, and rank set sampling estimation methods were applied with real-life data.


[1] M. Ahsan, Kumaraswamy exponentiated inverse Rayleigh distribution, Math. Theo. Model. 6 (3) (2016) 93-104.
[2] S. Ali, Mixture of the inverse Rayleigh distribution: Properties and estimation in a Bayesian framework, Appl. Math. Model. 39(2) (2015) 515–530.
[3] M.G. Bader and A.M. Priest, Statistical aspects of fibre and bundle strength in hybrid composites, Prog. Sci. Eng. Compos. (1982) 1129–1136.
[4] G.M. Cordeiro, E. M. M. Ortega, and A. J. Lemonte, The exponential–Weibull lifetime distribution, J. Stat. Comput. Simul. 84(12) (2014) 2592–2606.
[5] K. Fatima, S. Naqash, and S.P. Ahmad, Exponented generalized inverse Rayleigh distribution with applications in medical sciences, Pak. J. Stat. 34(5) (2018) 425–439.
[6] K. Fatima and S. P. Ahmad, Weighted Inverse Rayleigh Distribution, Int. J. Stat. Syst. 12(1) (2017) 119–137.
[7] T.G. Ieren and J. Abdullahi, Properties and applications of a two-parameter inverse exponential distribution with a decreasing failure rate, Pakistan J. Stat. 36(3) (2020).
[8] A. Joukar, M. Ramezani, and S.M.T.K. Mirmostafaee, Communications in Statistics - Theory and Methods Parameter estimation for the exponential-Poisson distribution based on ranked set samples, Commun. Stat. Theory Meth. 0(0) (2019) 1–22.
[9] A.S. Malik and S.P. Ahmad, A New inverse Rayleigh distribution: Properties and application, Int. J. Sci. Res. Math. Stat. Sci. 5 (2018) 92–96.
[10] M.J. Mohammed and I.H. Hussein, Some estimation methods for new mixture distribution with simulation and application [c], IOP Conf. Ser.: Mater. Sci. Engin. 571(1) (2019) 12014.
[11] S. Nasiru, Serial Weibull Rayleigh distribution: Theory and application, Int. J. Comput. Sci. Math. 7(3) (2016) 239–244.
[12] Y.P.E. Oguntunde, A.O. Adejumo and E.A. Owoloko, Exponential inverse exponential (EIE) distribution with applications to lifetime data, Asian J. Sci. Res. 10 (2017) 169–177.
[13] P. E. Oguntunde, A. O. Adejumo and O. S. Balogun, Statistical properties of the Eeponentiated generalized inverted exponential distribution, Appl. Math. 4 (2) (2014) 47–55.
[14] G.S. Rao and S. Mbwambo, Exponentiated inverse Rayleigh distribution and an application to coating weights of iron sheets data, J. Probab. Stat. 2019.
[15] R.A. Zeineldin, M. Ahsan and S. Hashmi, Research article type II half logistic Kumaraswamy distribution with applications, J. Func. Space 2020 (2020).
Volume 12, Issue 1
May 2021
Pages 935-944
  • Receive Date: 29 November 2020
  • Revise Date: 12 March 2021
  • Accept Date: 17 March 2021