Modelling and Interpreting of Exponentiated Stretched Exponential Distribution

Year 2023, , 451 - 470, 01.03.2023

Gulshan Majid , Ahmad Akhter

https://doi.org/10.35378/gujs.886208

Abstract

An innovative model titled as Exponentiated stretched exponential distribution is introduced. The main statistical properties of subject distribution are derived and special models are particularized. The most general technique of maximum likelihood estimation is focused to obtain the parameter estimates of new innovative model. A simulation study is presented to evaluate the behavior of the proposed estimators. Asymptotic confidence intervals for unknown parameters of new model are also suggested. The characterization of model is also checked. The competency of the subject distribution is demonstrated by fitting four real data sets through evaluation criteria.

Keywords

Exponentiation, Quantile function, Characterization, Simulation, Evaluation criteria

Supporting Institution

University of the Punjab, Pakistan

Project Number

870189

Thanks

Kind Regards

References

• [1] Johnson, N.L., Kotz, S. and Balakrishnan, N., “Continuous Univariate Distributions”, 2nd edn. Wiley, New York, (1994).
• [2] Eugene, N., Lee, C. and Famoye, F., “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 some tractability advantages”, Statistical Methodology, 6: 70–91, (2009).
• [4] Zografos, K. and Balakrishnan, N., “On families of beta- and generalized gammagenerated distributions and associated inference”, Statistical Methodology, 6: 344-362, (2009).
• [5] Kareema, A.K. and Abdalhussain, M.B., “Exponential Pareto Distribution”, Mathematical Theory and Modeling, 3: 135-150, (2013).
• [6] Alzaatreh, A., Lee, C. and Famoye, F., “A new method for generating families of continuous distributions”, Metron, 71: 63-79, (2013).
• [7] Bourguignon, M., Silva, R. B. and Cordeiro, G.M., “The Weibull-G family of probability distributions”, Journal of Data Science, 12:53-68, (2014).
• [8] Akinsete, A., Famoye, F. and Lee, C., “The beta-Pareto distribution”, Statistics, 42(6): 547-563, (2008).
• [9] Cordeiro, G. M., Cristino, C.T., Hashimoto, E.M., and Ortega, E.M., “The beta generalized Rayleigh distribution with applications to lifetime data”, Statistical Papers, 54: 133-161, (2013).
• [10] El-Bassiouny,A.H., Abdo,N.F. and Shahen,H.S., “Exponential Lomax Distribution”, International Journal of Computer Applications, 121: 24-29, (2015).
• [11] Nasiru, S. and Luguterah, A., “The new weibull-pareto distribution”, Pakistan Journal of Statistics and Operation Research, 11: 103-114, (2015).
• [12] Muhammad, T. and Saralees, N., “Parameter induction in continuous univariate distributions: Well-established G families”, Anais da Academia Brasileira de Ciências (Annals of the Brazilian Academy of Sciences), 87:539-568, (2015).
• [13] Gupta, R.C., Gupta, P.L. and Gupta, R.D., “Modeling failure time data by Lehmann alternatives”, Communications in Statistics - Theory and Methods, 27: 887-904, (1998).
• [14] Gupta, R.D. and Kundu, D., “Exponentiated Exponential Family: An Alternative to Gamma and Weibull Distributions”, Biometrical Journal, 43: 117–130, (2001).
• [15] Pal, M., Ali, M.M. and Woo, J., “Exponentiated Weibull Distribution”, Statistica, anno LXVI , 2: 130-147, (2006).
• [16] Masoom, A.M., Manisha, P. and Jungsoo, W., “Some Exponentiated Distributions”, The Korean Communications in Statistics, 14: 93–109, (2007).
• [17] Zakaria, A.J., “Exponentiated Exponential Distribution as a Failure Time Distribution”, Iraqi Journal of Statistical Science, 14: 63-75, (2008).
• [18] Shawky, A.I. and Bakoban, R.A., “Exponentiated Gamma Distribution: Different Methods of Estimations”, Journal of Applied Mathematics, 2012: 1-23, (2012).
• [19] Huang, S. and Oluyede, B.O., “Exponentiated Kumaraswamy-Dagum Distribution with Applications to Income and Lifetime Data”, Journal of Statistical Distributions and Applications, 8: 1-20, (2014).
• [20] Abu-Youssef, S.E., Mohammed, B.I. and Sief, M.G., “An Extended Exponentiated Exponential Distribution and its Properties”, International Journal of Computer Applications (0975 – 8887), 121: 1-6, (2015).
• [21] Afify, A.Z., Nofal, Z.M. and Ebraheim, A.N., “Exponentiated transmuted generalized Rayleigh distribution: a new four parameter Rayleigh distribution”, Pakistan Journal of Statistics and Operation Research, 11: 115-134, (2015).
• [22] Ahmed, A., Haitham, M., Yousof, H.M., Hamedani, G.G., and Aryal G.R., “The Exponentiated Weibull-Pareto Distribution with Application”, Journal of Statistical Theory and Applications, 15: 326-344, (2016).
• [23] Mohammed, E., Ibrahim, E., Gholam, H. and Amal, H., “On the Exponentiated Weibull Rayleigh Distribution”, Gazi University Journal of Science, 32(3): 1060-1081, (2019).
• [24] Laherr`ere, J. and Sornette, D., “Stretched exponential distributions in nature and economy: “fat tails” with characteristic scales”, European. Physical Journal B-Condensed Matter and Complex Systems, 2: 525–539, (1998).
• [25] Galambos, J. and Kotz, S., “Characterizations of probability distributions. A unified approach with an emphasis on exponential and related models”, Lecture Notes in Mathematics, 675, (1978).
• [26] Ahsanullah, M., Shakil, M. and Golam Kibria, B.M., “Characterizations of Continuous Distributions by Truncated Moment”, Journal of Modern and Applied Statistical Methods, 15(1): 316-331, (2016).
• [27] Majid, G. A. and Akhter, A. S., “Model specification and data interpretation of climate in Pakistan”, Modeling Earth Systems and Environment, 1-45, (2021).