The alpha power Weibull Frechet distribution: properties and applications

Abstract

Modeling everyday life processes play a great role in human existence. Thus, distribution theory has helped to understand how our everyday life processes are distributed. However, this depends on how researchers in distribution theory compound several distributions to derive a more flexible distribution. This study proposes the alpha power Weibull Frechet distribution for real-life datasets. However, some statistical structural properties of the model such as kurtosis, hazard rate and odd functions, cumulative, quantiles, reversed hazard, skewness, order statistics and survival function were derived. The parameters of the proposed model were obtained using the maximum likelihood method. The behavioural nature of the model was studied through simulation. Finally, a two real life data was used to investigate the performance of the proposed model. The results show that the new model performs better than some existing continuous models in statistical literature.

Keywords

• Alpha power,Compounding,Maximum likelihood,Statistical analysis,Weibull Frechet.

References

1. Johnson NL. Systems of frequency curves generated by methods of translation. Biometrika 1949; 36:149-176.
2. Tukey JW. The practical relationship between the common transformations of percentages of counts and amounts. Technical report 36. Princeton University, Princeton N J, Statistical Technique Research Group.
3. Lee C, Famoye F, Alzaatreh AY. Methods for generating families of univariate continuous distributions in the recent decades. Wiley Interdisciplinary Reviews: Computational Statistics 2013; 5 (3), 219 - 238.
4. Weibull W. A statistical distribution functions of wide applicability. Journal of Applied Mechanics, Transactions 1951; 18: 293-297.
5. Afify AZ, Yousof HM, Cordeiro GM, Ortega EMM, Nofal ZM. The Weibull Frechect distribution and its applications. Journal of Applied Statistics 2016. Doi.org/10.1080/02664763.2016.1142945
6. Mahdavi A, Kundu D. A new method for generating distributions with an application to exponential distribution. Communications in Statistics - Theory and Methods 2017; 46 (13): 6543 - 6557.
7. Bourguignon MB, Silva R. Cordeiro, GM. The Weibull-G family of probability distributions. Journal of Data Science 2014; 12:53 - 68.
8. Unal C, Cakmakyapan S, Ozel G. Alpha Power Inverted Exponential Distribution: Properties and Application, Gazi University Journal of Science 2018; 31(3): 954-965.

9. Alizadeh M, Cordeiro GM, Pinho LGB, Ghosh I. The Gompertz-G family of distributions, Journal of Statistical Theory and Practice 2017; 11(1), 179-207.
10. Eghwerido JT, Zelibe SC, Efe-Eyefia E. Gompertz alpha power inverted exponential: properties and applications 2020a; Article in the press. [11] Eghwerido JT, Zelibe SC, Ekuma-Okereke E, Efe-Eyefia E.
11. On the extended new generalized exponential distribution: properties and applications. FUPRE Journal of Scientific and Industrial Research 2019; 3(1), 112-122.
12. Efe-Eyefia E, Eghwerido JT, Zelibe SC. Weibull alpha power inverted exponential Distribution: properties and applications. Gazi University Journal of Science, 2020; forthcoming.
13. Nassar M, Alzaatreh A, Mead A, Abo-Kasem O. Alpha power Weibull distribution: Properties and applications. Communications in Statistics-Theory and Methods 2017:46, 10236 - 10252.
14. Smith RL, and Naylor J. C. A comparison of maximum likelihood and Bayesian estimates for the three-parameter Weibull distribution. Applied Statistics 1987; 36:258-369.
15. Haq MA, Butt NS, Usman RM, Fattah AA. Transmuted power function distribution, Gazi University Journal of Science 2016: 29(1):177-185.
16. Merovci F, Khaleel M, AIbrahim NA, Shitan M. The beta type-X distribution: properties with application. Springer-Plus 2016; 5, 697.
17. Rastogi MK, Oguntunde PE. Classical and bayes estimation of reliability characteristics of the Kumaraswamy-inverse exponential distribution. International Journal of System Assurance Engineering and Management 2017.
18. Oguntunde PE, Khaleel MA, Ahmed MT, Adejumo AO, Odetunmibi OA. A new generalization of the Lomax distribution with increasing, decreasing, and constant failure rate. Hindawi Modelling and Simulation in Engineering 2017, 1-7.
19. Nichols MD, Padgett WJ. A bootstrap control chart for Weibull percentiles. Quality and Reliability Engineering International 2006; 22:141-151.