The Gompertz extended generalized exponential distribution: properties and applications

Year 2020, , 739 - 753, 30.06.2020

J. T. Eghwerido , Lawrence Nzeı , Ikwuoche John Davıd Obinna Damian Adubısı

https://doi.org/10.31801/cfsuasmas.602930

Cited By: 10

Abstract

In this article,  a new class of distribution in the exponential family of distributions called the Gompertz extended generalized exponential distribution (G-EGE) for life time processes is proposed. The mathematical properties of the G-EGE distribution such as the reliability, hazard rate function, reversed hazard, cumulative. odd functions, quantiles function, kurtosis, skewness and order statistics were derived. The parameter estimates of the G-EGE distribution were estimated using the maximum likelihood estimation method. The efficiency and flexibility of the G-EGE distribution were examined using a simulation study and a real life data application. The results revealed that the G-EGE distribution outperformed some of the existing distributions considered in this study.

Keywords

Exponential distribution, Extended generalized exponential distribution

References

• Lee, C., Famoye, F. and Alzaatreh A. Y. Methods for generating families of univariate continuous distributions in the recent decades, Wiley Interdisciplinary Reviews: Computational Statistics, 5(3) (2013) 219 - 238.
• Keller, A. Z., Kamath, A. R. R. and Perera, U. D. Reliability analysis of CNC machine tools, Reliability Engineering, 3(6) (1982) 449 - 473.
• Lin, C. T., Duran, B. S. and Lewis, T. O. Inverted gamma as a life distribution, Microelectronics Reliability, 29(4) (1989) 619 - 626.
• Oguntunde, P. E. and Adejumo, A. The transmuted inverse exponential distribution, International Journal of Advanced Statistics and Probability, 3 (1), (2014a) 1 - 7.
• Oguntunde, P. E., Adejumo, A., and Balogun, O. S. Statistical properties of the exponentiated generalized inverted exponential distribution, Applied Mathematics, 4 (2) (2014) 47 - 55. Oguntunde, P. E., Babatunde, O. S., Ogunmola, A. O. Theoretical analysis of the Kumaraswamy-inverse exponential distribution, International Journal of Statistics and Applications, 4 (2), (2014c) 113 - 116.
• Olapade, A. K. On Extended generalized exponential distribution, British Journal of Mathematics and Computer Science, 4(9) (2014) 1280-1289.
• Pinho, L. G. B., Cordeiro, G. M. and Nobre, J. S. The Harris extended exponential distribution, Communications in Statistics -Theory and Methods, 44(16) (2015) 3486 - 3502.
• Fatima, A. and Roohi, A. Extended Poisson exponential distribution, Pakistan Journal of Statistics and Operation Research, 11(3), (2015) 361-375.
• Anake, T. A., Oguntunde, F. E. and Odetunmibi, A. O. On a fractional beta-exponential distribution, International Journal of Mathematics and Computations, 26(1) (2015) 26 - 34.
• Thiago, A. N. de-Andrade, M. Bourguignon, M. B. and Cordeiro, G. M. The exponentiated generalized extended exponential distribution, Journal of Data Science, 14, (2016) 393-414
• Nadarajah, S. and Okorie, I. E. On the moments of the alpha power transformed generalized exponential distribution, Ozone: Science and Engineering, (2017) 1 - 6.
• Mahdavi, A. and Jabari, L. An Extended Weighted Exponential Distribution, Journal of Modern Applied Statistical Methods, 16(1) (2017) 296-307.
• Hamedani, G. G., Yousof, H. M., Rasekhi, M., Alizadeh, M. and Najibi, M. S. Type I general exponential class of distributions, Pakistan Journal of Statistics and Operation Research, 14(1), (2018) 39-55.
• Eghwerido, J. T., Zelibe, S. C and Efe-Eyefia, E. Gompertz-Alpha power inverted exponential distribution: properties and applications. Journal of Thailand Statisticians, (2019). Article in the press.
• Eghwerido, J. T., Zelibe, S. C., Ekuma-Okereke, E. and Efe-Eyefia, E. On the Extended New Generalized Exponential Distribution: Properties and Applications. FUPRE Journal of Scientific and Industrial Research, 3 (1), (2019a) 112-122.
• Eghwerido, J. T., Nzei, L. C. and Agu, F. I. Alpha power Gompertz distribution: properties and applications, Sankhya A - The Indian Journal of Statistics 2020. Article in the press.
• Afify, A. Z., Altun, E., Yousof, H. M., Alizadeh, M., Ozel, G. and Hamedani, G. G. The odd exponentiated half-logistic-G family: properties, characterizations and applications, Chilean Journal of Statistics, 8(2) (2017) 65 - 91.
• Al-Moflel, H. On generating a new family of distributions using the tangent function, Journal of Statistics and operation Research, 3 (2018) 471 - 499.
• Gupta, R. C. and Kundu, D. Generalized exponential distribution. Australian and New Zealand Journal of Statistics, 41 (2001) 173 - 188.
• Unal, C., Cakmakyapan, S., and Ozel, G. Alpha power inverted exponential distribution: Properties and application, Gazi University Journal of Science, 31 (3), (2018) 954 - 965.
• Nassar, M., Alzaatreh, A., Mead, A. and Abo-Kasem, O. Alpha power Weibull distribution: Properties and applications, Communications in Statistics-Theory and Methods, 46 (2017) 10236 - 10252.
• Dey, S., Alzaatreh, A., Zhang, C. and Kumar, D. A new extension of generalized exponential distribution with application to ozone data, Ozone: Science and Engineering, 39(4) (2017) 273 - 285.
• Yousof, H. M, Afify, A. Z., Alizadeh, M., Butt, N. S., Hamedani, G. G. and Ali M. M. The transmuted exponentiated generalized-G family of distributions, Pakistan Journal of Statistics and operation Research, 11(4) (2015) 441 - 464.
• Aryal, G. R. and Yousof, H. M. The exponentiated generalized-G Poisson family of distributions, Economic Quality Control, 32(1) (2017) 1 - 17.
• Cordeiro, G. M., Ortega, E. M. and da-Cunha, D. C. C. The exponentiated generalized class of distributions, Journal of Data Science, 11 (2013) 1 - 27.
• Mahdavi, A. and Kundu, D. A new method for generating distributions with an application to exponential distribution, Communications in Statistics - Theory and Methods, 46(13) (2017) 6543 - 6557.
• Abouammoh, A. M. and Alshingiti, A. M. Reliability estimation of generalized inverted exponential distribution, Journal of Statistical Computation and Simulation, 79(11) (2009) 1301 - 1315.
• Alizadeh, M., Cordeiro, G. M., Pinho, L. G. B. and Ghosh, I. The Gompertz-G family of distributions, Journal of Statistical Theory and Practice, 11(1) (2017) 179 - 207.
• Smith, R, L., and Naylor, J. C. A comparison of maximum likelihood and bayesian estimators for the three-parameter Weibull distribution, Applied Statistics, 36, (1987) 258 - 369.
• Haq, M. A., Butt, N. S., Usman, R. M. and Fattah, A. A. Transmuted power function distribution, Gazi University Journal of Science, 29(1) (2016) 177 - 185.
• Bourguinon, M. B., Silva, R. and Cordeiro, G. M. The Weibull-G family of probability distributions, Journal of Data Science, 12 (2014) 53 - 68.
• Merovci, F., Khaleel, M. A., Ibrahim, N. A. and Shitan, M. The beta type-X distribution: properties with application, Springer-Plus, 5, (2016) 697.
• Rastogi, M. K. and Oguntunde, P. E. Classical and bayes estimation of reliability characteristics of the Kumaraswamy-inverse exponential distribution. International Journal of System Assurance Engineering and Management, 2018.
• Efe-Eyefia, E., Eghwerido, J. T. and Zelibe, S. C. Weibull-Alpha power inverted exponential distribution: properties and applications, Gazi University Journal of Science, (2019), forthcoming.
• Zelibe, S. C., Eghwerido, J. T. and Efe-Eyefia, E. Kumaraswamy-Alpha power inverted exponential distribution: properties and applications, Istatistik Journal of the Turkish Statistical Association, 12(2) (2019) 35 -48.