American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2019, 7(5), 178-186
DOI: 10.12691/ajams-7-5-4
Open AccessArticle

Exponentiated Gumbel Exponential Distribution: Properties and Applications

Uchenna U Uwadi1, , Emmanuel W Okereke2 and Chukwuemeka O Omekara2

1Department of Mathematics/Computer Science/Statistics/Informatics, Alex Ekwueme Federal University Ndufu-Alike Ikwo, Nigeria

2Department of Statistics, Micheal Okpara University of Agriculture, Umudike, Nigeria

Pub. Date: November 12, 2019

Cite this paper:
Uchenna U Uwadi, Emmanuel W Okereke and Chukwuemeka O Omekara. Exponentiated Gumbel Exponential Distribution: Properties and Applications. American Journal of Applied Mathematics and Statistics. 2019; 7(5):178-186. doi: 10.12691/ajams-7-5-4


In this article, we proposed a new distribution called exponentiated Gumbel exponential (EGuE) distribution. The new distribution is a member of the T-X family obtained through the logit transformation of the exponential random variable, using the exponentiated Gumbel distribution as the generator. The mathematical properties of the proposed distribution were studied. The maximum likelihood estimates of the parameters of the EGuE distribution were derived. The applicability of the new distribution is shown using a real data set.

exponentiated Gumbel distribution T-X family maximum likelihood estimation logit function exponential distribution

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[1]  Lee, C., Famoye, F. and Alzaatreh, A, “Methods of generating families of univariate continuous distributions in the recent decades”. WIRESs Computational Statistics, 5. 219-238. 2013.
[2]  Eugene, N., Lee, C. and Famoye F, “A beta Beta-normal distribution and its applications”. Communications in Statistics. Theory and Methods 31 (4), 497-512. 2002.
[3]  Jones, M.C, “Kumaraswamy’s distribution: a beta-type distribution with tractability advantages”. Statistical Methodology 6, 70-81. 2009.
[4]  Cordeiro, G. M., and de Castro, M “A new family of generalized distributions.” Journal of Statistical Computation and Simulations 81 (7). 833-898. 2011.
[5]  Gupta, R.C., Gupta, P.L. and Gupta, R.D, “Modeling failure time data by Lehman alternatives”. Communications in Statistics- Theory and Methods 27(4) .887-904. 1998.
[6]  Shaw, W, I., and Buckley, I, R “The alchemy of probability distributions: beyond Gram-charlier expansion, and a skew-kurtitic-normal distribution from a rank transmutation map” arxiv print, arXiv: 0901.0434. 2009.
[7]  Alizadeh , M, Merovci F. and Hamedani , G G , “Generalized Transmuted Family of Distributions: Properties and Applications”. Hacettepe journal of Mathematics and Satatistics. 46 (4), 2017.
[8]  Alzaatreh, A., Lee, C. and Famoye, F, “A new method for generating families of continuous distributions”, Metron 71(1), 63-79. 2013.
[9]  Nadarajah, S, “The exponentiated Gumbel distribution with climate application”. Environmetrics 17. 13-23. 2006.
[10]  Galton, F. Enquires into human faculty and its development. Macmillan and company London. 1983.
[11]  Moor J.J “A quantile alternative for kuutosis”. The Statistician 37, 25-32 .1988.
[12]  Alizadeh, M., Cordeiro, G. M., de Brito, E. and Demetrio, C .B, “The beta Marshall-Olkin family of distributions”, Journal of Statistical distributions and Applications 2 (4). 2015.
[13]  Elgarhy, M., Shakil, M. and Kibria, B.M., “Exponentiated Weibull-exponential distribution with applications”, Applications and Applied Mathematics: An International journal, 12. 710-725. 2017.
[14]  Oguntunde, P.E., Balogun, O.S., Okagbue, H.I. and Bishop, S.A., “The Weibull-exponential distribution: its properties and applications”, Journal of Applied Statistics. 15. 1305-1311. 2015
[15]  Bjerkedal, T., “Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli”, American Journal of Epidemilology, 72(1). 130-148.1960.