Article Sidebar

Download
PDF
Statistic
Read Counter : 562 Download : 570

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Main Article Content

Abstract

In this paper, we propose a new flexible lifetime distribution. The proposed distribution will be referred to as beta power Muth distribution. It can be used to model increasing, decreasing, bathtub shaped or upside-down bathtub hazard rates. Some properties of the new model are obtained including moments, quantile function and moments of the order statistics. The unknown model parameters are estimated by the maximum likelihood method of estimation. A Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates. Two reliability data sets are applied to illustrate the usefulness and flexibility of the proposed model. In addition, we introduce a new location-scale regression model based on the logarithm of the proposed distribution and provide a real data application.

Keywords

Beta distribution Muth distribution regression modeling maximum likelihood estimation data analysis

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following License

CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.

 

How to Cite
Benkhelifa, L. (2022). The Beta Power Muth Distribution: Regression Modeling, Properties and Data Analysis. Pakistan Journal of Statistics and Operation Research, 18(1), 225-243. https://doi.org/10.18187/pjsor.v18i1.3529
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Aarset, M. V. (1987). How to identify a bathtub hazard rate. IEEE Transactions on Reliability, 36(1), 106-108.
  2. Ahmad, A. A. Ghazal M. G. M. (2020). Exponentiated additive Weibull distribution. Reliability Engineering and System Safety 193, 106663.
  3. Awodutire P. O., Nduka E. C., Ijomah M. A. (2020). The beta type I generalized half logistic distribution: properties and application. Asian Journal of Probability and Statistics, 6(2), 27-41.
  4. Alizadeh M., Altun E., Cordeiro G. M., Rasekhi M. (2018). The odd power cauchy family of distributions: properties, regression models and applications. Journal of Statistical Computation and Simulation, 88(4), 785-807.
  5. Aryall G.R., Tsokos C.P. (2011). Transmuted Weibull distribution: A generalization of the Weibull probability distribution. European Journal of Pure and Applied Mathematics, 2, 89-102.
  6. Benkhelifa L. (2017). The beta generalized Gompertz distribution. Applied Mathematical Modelling, 52, 341-357.
  7. Benkhelifa L. (2021). The beta reduced modified Weibull distribution with applications to reliability data. Journal of Reliability and Statistical Studies, 14(1), 323-352.
  8. Cordeiro G. M., Ortega E.M., Nadarajah S. (2010). The Kumaraswamy Weibull distribution with application to failure data. Journal of The Franklin Institute, 347, 1399-1429.
  9. Corderio G.M., Hashimoto E.H., Ortega, E.M.M. (2014). The McDonald Weibull model. Statistics, 48, 256-278.
  10. Eugene N., Lee C., Famoye F. (2002). Beta-normal distribution and its applications. Commun. Stat. Theor. M., 31, 497-512.
  11. Famoye F., Lee C., Olumolade O. (2005). The beta-Weibull distribution. J. Stat. Theor. Applic., 4(2), 121-136.
  12. Fleming T.R., Harrington D.P., Counting Process and Survival Analysis, John Wiley, New York, NY, USA, 1994.
  13. Gradshteyn I.S., Ryzhik I.M. Table of Integrals, Series and Products. Academic Press, New York, 2000.
  14. Hosmer D.W., Lemeshowik S. Applied survival analysis: regression modeling of time to event data. New York: JohnWiley Son, 1999.
  15. Irshad M. R., Maya R., Krishna A. (2021). Exponentiated power Muth distribution and associated inference. Journal of the Indian Society for Probability and Statistics, 22, 265-302.
  16. Jodrá P., Gómez H.W., Jiménez-Gamero M.D., Alba-Fernández M.V. (2017). The power Muth distribution. Math. Model. Anal., 22(2), 186-201.
  17. Jodrá P. J, Jiménez-Gamero M.D., Alba-Fernández M.V. (2015). On the Muth distribution. Math. Model. Anal., 20(3), 291-310.
  18. Leemis L.M., McQueston J.T. (2008). Univariate distribution relationships. Am. Stat., 62(1), 45-53.
  19. Milgram M.S. (1985). The generalized integro-exponential function. Math. Comp., 44(170), 443-458.
  20. Muth E.J. (1977). Reliability models with positive memory derived from the mean residual life function. In C.P. Tsokos and I. Shimi (Eds.), The Theory and Applications of Reliability, volume 2, pp. 401-435, New York,. Academic Press, Inc.
  21. Nadarajah S., Kotz S.(2005). The beta exponential distribution. Reliab. Eng. Syst. Saf., 91, 689-697.
  22. Nassar M., Alzaatreh A., Mead M., Abo-Kasem O. (2017). Alpha power Weibull distribution: properties and applications, Commun. Stat.-Theory Methods, 46, 10236-10252.
  23. Prataviera F., Ortega E.M.M., Cordeiro G.M., Pescim R.R., Verssania B.A.W. (2018). A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems. Reliab Eng Syst Saf, 176,13-26.
  24. Proschan F. (1963). Theoretical explanation of observed decreasing failure rate. Technometrics; 5, 375-383.
  25. Shakhatreh M.K., Yusuf A., Mugdadi A. (2016). The beta generalized linear exponential distribution. Statistics, 50(6), 1346-1362.
  26. Singla N., Jain K., Sharma S. K.(2012). The beta generalized Weibull distribution: properties and applications. Reliab. Eng. Syst. Saf., 102, 5-15.
  27. Therneau T.M., Grambsch, P.M., Fleming, T.R. (1990). Martingale-based residuals for survival models. Biometrika, 77, 147-160.