ON DEVELOPMENT OF FOUR-PARAMETERS EXPONENTIATED GENERALIZED EXPONENTIAL DISTRIBUTION
Keywords:
Moment, Hazard rate., Kurtosis., Renyi Entropy., Unimodal
Abstract
In this paper a four parameter Exponentiated Generalized Exponentiated exponential distribution Is derived from family of GEE and studied. Various properties of the distribution are studied. The distribution is found to be unimodal and has a decreasing and increasing hazard rate depending on the shape parameters. The expressions for the moment, median, quartile, mean deviation, median deviation, skeweness, kurtosis, Renyi entropy are obtained. Several known continuous distributions are found to be special cases of the new distributions. Simulation study and maximum likelihood estimate are used to estimate unknown parameters.
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Kumaraswamy distribution and its log-transformation Brazilian journal of probability
and, vol.27,No 1,31-53
[2] Gompertz, B. (1825), “On the nature of the function expressive of the law of human
mortality, and on a new mode of determining the value of life
contingencies”,Philosophical Transactions of the Royal Society London, vol. 115, 513 -
585.
[3] Verhulst, P. F. (1838), “Notice sur la loi la population suit dans son accroissement”,
Correspondence mathematiqueet physique, publiee L. A. J. Quetelet, vol. 10, 113 121.
[4 ] Verhulst, P. F. (1845), “Recherches mathematiquessur la loi-d’-accroissementdela
population”, Nouvelles Memoires de l’Academie Royale des Sciencset Belles Lettres de
Bruxelles [i.e. Memoires, Series 2], vol. 18, 38 pp.
[5] Verhulst, P. F. (1847), “Deuxieme memoire sur la loid’accroissement de la population”,
Memoires de l’Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique,
Series 2, vol. 20, 32 pp.
[6] Ahuja, J. C. and Nash, S. W. (1967), “The generalized Gompertz-Verhulst family of
distributions”, Sankhya, Ser. A., vol. 29, 141 - 156.
[7] Mudholkar, G.S. and Srivastava, D.K. (1993). Exponentiated Weibull family for
analyzing bathtub failure rate data, IEEE Transactions on Reliability, 42(2), 299 - 302.
[8] Gupta, R. C., Gupta, P. L., and Gupta, R. D., 1998: Modeling failure time data by
Lehman alternatives. Communications in Statistics, Theory and Methods 27, 887–904.
[9] Gupta, R.D. and Kundu, D. (1999). Generalized exponential distributions. Australian &
New Zealand Journal of Statistics, 41(2), 173 - 188.
[10] Cordeiro, G. M., Ortega, E. M. M., & Cunha, D. C. C. (2013). The exponentiated
generalized class of distributions. Journal of Data Science, 11, 1C27.
[11] Lehmann, E. L. (1953). The power of rank tests. Annals of Mathematical Statistics,
24:23– 43.
[12] Nadarajah, S. and Kotz, S. (2006). The beta exponential distribution, Reliability
Engineering and System Safety, 91(6), 689 - 697.
[13] Cordeiro, G. M., &Lemonte, A. J. (2014). The exponentiated generalized BirnbaumSaunders distribution. Applied Mathematics and Computation, 247, 762C779.
https://doi.org/10.1016/j.amc.2014.09.054.
[14] Cordeiro, G. M., Gomes, A. E., & da-Silva, C. Q. (2014). Another extended Burr III
model: some properties and applications. Journal of Statistical Computation and
Simulation, 84, 2524C2544. https://doi.org/10.1080/00949655.2013.793343.[15] Elbatal, I. and Muhammed, H. Z. (2014). Exponentiated generalized inverse
Weibulldistribu- tion. Applied Mathematical Sciences, 8:3997–4012.
,
[16] Oguntunde, P. E., Adejumo, A. O., and Balogun, O. S. (2014). Statistical properties of
the exponentiated generalized inverted exponential distribution. Applied Mathematics,
4:47– 55.
[17] Da Silva, R. V., Gomes-Silva, F., ..., &Cordeiro, G. M. (2015). A new extended gamma
generalized model. International Journal of Pure and Applied Mathematics, 100,
309C335. https://doi.org/10.12732/ijpam.v100i2.11
[18] De Andrade, T. A. N., Bourguignon, M., &Cordeiro, G. M. (2016). The exponentiated
generalized extended exponential distribution. Journal of Data Science, 14, 393C414.
[19] De Andrade, T. A. N., Rodrigues, H., ..., & Cordeiro, G. M. (2015). The exponentiated
generalizedGumbel distribution. Revista
Colombiana de Estadstica, 38, 123C143.https://doi.org/10.15446/rce.v38n1.48806
[20] Cordeiro G. M., de Andrade T.M, Bourguignon M. & Gomes-SilvaF. The
Exponentiated Generalized Standardized Half-logistic
Distribution International Journal of Statistics and Probability; Vol. 6, No. 3; May 2017
ISSN 1927-7032 E-ISSN 1927-7040
[21] Alzaatreh, A., Lee, C., and Famoye, F. (2013a). A new method for generating families of
continuous distributions, Metron, 71(1), 63 - 79.
[22] Johnson, N.L., Kotz, S., Balakrishnan, N (1994).: Continuous Univariate Distributions,
vol. 1, 2nd edn. Wiley, New York.
[23] Galton, F. (1883). Enquiries into Human Faculty and its Development, Macmillan and
Company, London
[24] Moor, J.J. (1988). A quantile alternative for Kurtosis, The Statistician, 37, 25 - 32
Published
2018-08-30
How to Cite
A., & G. M,. (2018). ON DEVELOPMENT OF FOUR-PARAMETERS EXPONENTIATED GENERALIZED EXPONENTIAL DISTRIBUTION. GPH-International Journal of Applied Science, 1(1), 20-39. Retrieved from https://gphjournal.org/index.php/as/article/view/95
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