##### Title: A New Generalized Exponential Distribution: Properties and Applications

##### Pages: 799-818

##### Cite as:

Jawad Hussain Ashraf, Munir Ahmad, A. Khalique, Zafar Iqbal, A New Generalized Exponential Distribution: Properties and Applications, Int. J. Anal. Appl., 18 (5) (2020), 799-818.#### Abstract

The exponential distribution is a popular statistical distribution to study the problems in lifetime and reliability theory. We proposed a new generalized exponential distribution, wherein exponentiated exponential and exponentiated generalized exponential distributions are sub-models of the proposed distribution. We study several important statistical and mathematical properties of the newly developed model and provide the simple expressions for the generating function, moments and mean deviations. Parameters of the proposed distribution are estimated by the technique of maximum likelihood. For two real data sets from the field of biology and engineering, the proposed distribution is compared to some existing distributions. It is found that the proposed model is more suitable and useful to study lifetime data. Thus, it gives us another alternative model for existing models.

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#### References

- W. Barreto-Souza, A.H.S. Santos, G.M. Cordeiro, The beta generalized exponential distribution, J. Stat. Comput. Simul. 80 (2010), 159–172.
- R.S. Chhikara, J.L. Folks, The Inverse Gaussian Distribution as a Lifetime Model, Technometrics. 19 (1977), 461–468.
- G.M. Cordeiro, E.M. Ortega, D.C. da Cunha, The exponentiated generalized class of distributions, J. Data Sci. 11 (2013), 1–27.
- P. R. Diniz Marinho, M. Bourguignon, and C. R. Barros Dias, AdequacyModel: Adequacy of Probabilistic Models and General Purpose Optimization, R package version 2.0.0. 2016. https://cran.r-project.org/package=AdequacyModel
- R.C. Gupta, P.L. Gupta, R.D. Gupta, Modeling failure time data by lehman alternatives, Commun. Stat. Theory Methods. 27 (1998), 887–904.
- R.D. Gupta, D. Kundu, Theory & Methods: Generalized exponential distributions, Aust. N.Z. J. Stat. 41 (1999), 173–188.
- R.D. Gupta, D. Kundu, Exponentiated exponential family: an alternative to gamma and weibull distributions, Biom. J. 43 (2001), 117–130.
- R.D. Gupta, Debasis. Kundu, Generalized exponential distribution: different method of estimations, J. Stat. Comput. Simul. 69 (2001), 315–337.
- R.D. Gupta, D. Kundu, Closeness of Gamma and Generalized Exponential Distribution, Commun. Stat. Theory Methods. 32 (2003), 705–721.
- R.D. Gupta, D. Kundu, Discriminating between Weibull and generalized exponential distributions, Comput. Stat. Data Anal. 43 (2003), 179–196.
- R.D. Gupta, D. Kundu, On the comparison of Fisher information of the Weibull and GE distributions, J. Stat. Plan. Inference. 136 (2006), 3130–3144.
- R.D. Gupta, D. Kundu, Generalized exponential distribution: Existing results and some recent developments, J. Stat. Plan. Inference. 137 (2007), 3537–3547.
- D. Kundu, R.D. Gupta, A. Manglick, Discriminating between the log-normal and generalized exponential distributions, J. Stat. Plan. Inference. 127 (2005), 213-227.
- C.D. Lai, D.N.P. Murthy, M. Xie, Weibull distributions, WIREs Comput. Stat. 3 (2011), 282–287.
- E.T. Lee, J.W. Wang, Statistical methods for survival data analysis, 3rd ed, J. Wiley, New York, 2003.
- G.S. Mudholkar, D.K. Srivastava, Exponentiated weibull family for analyzing bathtub failure-rate data, IEEE Trans. Reliab. 42 (1993), 299–302.
- S. Nadarajah, The exponentiated exponential distribution: a survey, AStA Adv. Stat. Anal. 95 (2011), 219–251.
- S. Nadarajah, S. Kotz, The beta exponential distribution, Reliab. Eng. Syst. Safety. 91 (2006), 689–697.
- S. Nadarajah, S. Kotz, The Exponentiated Type Distributions, Acta Appl. Math. 92 (2006), 97–111.
- R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2019.
- M.M. Raqab, M. Ahsanullah, Estimation of the location and scale parameters of generalized exponential distribution based on order statistics, J. Stat. Comput. Simul. 69 (2001), 109–123.
- M.Z. Raqab, Inferences for generalized exponential distribution based on record statistics, J. Stat. Plan. Inference. 104 (2002), 339–350.
- M.Z. Raqab, Generalized exponential distribution: Moments of order statistics, Statistics. 38 (2004), 29–41.
- M.M. Risti´c, D. Kundu, Marshall-olkin generalized exponential distribution, Metron. 73 (2015), 317–333.
- M.H. Tahir, S. Nadarajah, Parameter induction in continuous univariate distributions: Well-established g families, An. Acad. Bras. Ciˆenc. 87 (2015), 539–568.