[Home ] [Archive]    
:: Volume 16, Issue 1 (9-2019) ::
JSRI 2019, 16(1): 1-31 Back to browse issues page
A New Lifetime Distribution: The Beta Modified Weibull Power Series Distribution
Ehsan Bahrami *1, Narges Yarmoghaddam2
1- Shahid Beheshti Universiti , Samani
2- Shahid Beheshti University
Abstract:   (877 Views)

In this paper, we propose a new parametric distribution which called as the Beta Modified Weibull Power Series (BMWPS) distribution. This distribution is obtained by compounding Beta Modified Weibull (BMW) and power series distributions. BMWPS distribution contains, as special sub-models, such as Beta Modified Weibull Poisson (BMWP) distribution, Beta Modified Weibull Geometric (BMWG) distribution, Beta Modified Weibull Logarithmic (BMWL)

distribution, among others. We obtain closed-form expressions for the cumulative distribution, density, survival function, failure rate function, the r-th raw moment and the moments of order statistics. A full likelihood-based approach that allows yielding maximum likelihood estimates of the BMWPS  arameters is used. Finally, application to the Aarset data are given.
Keywords: Lifetime, Beta Modified Weibull distribution, power series distribution, maximum Likelihood estimation, hazard function, Fisher's information matrix
Full-Text [PDF 3561 kb]   (254 Downloads)    
Type of Study: Research | Subject: General
Received: 2019/05/23 | Accepted: 2020/03/12 | Published: 2020/05/23
References
1. Aarset, M.V. (1987). How to Identify Bathtub Hazard Rate. IEEE Transactions on Reliability, 36, 106-108. [DOI:10.1109/TR.1987.5222310]
2. Bagheri, S.F., Samani, E.B. and Ganjali, M. (2016). The Generalized Modified Weibull Power Series Distribution: Theory and Applications. Computational Statistics and Data Analysis, 94, 136-160. [DOI:10.1016/j.csda.2015.08.008]
3. Bebbington, M., Lai, C.D. and Zitikis, R. (2007). A Flexible Weibull Extension. Reliability Engineering and System Safety, 92, 719-726. [DOI:10.1016/j.ress.2006.03.004]
4. Barlow, R.E., Campo, R. (1975). Total Time on Test Processes and Applications to Failure Data Analysis. In: Reliability and Fault Tree Analysis. Society for Industrial and Applied Mathematics, 451-481.
5. Carrasco, J.M.F., Ortega, E.M.M. and Cordeiro, G.M. (2008). A Generalized Modified Weibull Distribution for Lifetime Modeling. Computational Statistics and Data Analysis: doi 10.1016/j.CSDA.2008.08.023. [DOI:10.1016/j.csda.2008.08.023]
6. Cordeiro, G.M., Simas, A.B. and Stoesiac, B.D. (2008). The Beta Weibull Distribution. Submitted to Journal of Statistical Computation and Simulation.
7. Glaser, R.E. (1980). Bathtub and Related Failure Rate Characterizations. Journal of the American Statistical Association, 75, 667-672. [DOI:10.1080/01621459.1980.10477530]
8. Haupt, E. and Schabe, H. (1992). A New Model for a Lifetime Distribution with Bathtub Shaped Failure Rate. Microelect. and Reliab, 32, 633-639. [DOI:10.1016/0026-2714(92)90619-V]
9. Hjorth, U. (1980). A Realibility Distribution with Increasing, Decreasing, Constant and Bathtub Failure Rates. Technometrics, 22, 99-107. [DOI:10.2307/1268388]
10. Lai, C.D., Xie, M. and Murthy, D.N.P. (2003). A Modified Weibull Distribution. Transactions on Reliability, 52, 33-37. [DOI:10.1109/TR.2002.805788]
11. Mudholkar, G.S. and Srivastava, D.K. (1993). Exponentiated Weibull Family for Analyzing Bathtub Failure-real Data. IEEE Trans Reliab, 42, 299-302. [DOI:10.1109/24.229504]
12. Mudholkar, G.S., Srivastava, D.K. and Friemer, M. (1995). The Exponentiated Weibull Family: A Reanalysis of the Bus-motor-failure Data. Technometrics, 37, 436-445. [DOI:10.1080/00401706.1995.10484376]
13. Mudholkar, G.S., Srivastava, D.K. and Kollia, G.D. (1996). A Generalization of the Weibull Distribution with Application to the Analysis of Survival Data. J. Amer. Statist. Assoc., 91, 1575-1583. [DOI:10.1080/01621459.1996.10476725]
14. Nadarajah, S. and Kotz, S. (2004). The Beta Gumbel Distribution. Mathematical Problems in Engineering, 323-332. [DOI:10.1155/S1024123X04403068]
15. Nelson, W. (1982). Lifetime Data Analysis. Wiley, New York. [DOI:10.1002/0471725234]
16. Pham, H. and Lai, C.D. (2007). On Recent Generalizations of the Weibull Distribution. IEEE Transactions on Reliability, 56, 454-458. [DOI:10.1109/TR.2007.903352]
17. Rajarshi, S. and Rajarshi, M.B. (1988). Bathtub Distributions: a Review. Comm. Statat. Theory. Meth., 17, 2521-2597. [DOI:10.1080/03610928808829761]
18. Silva, G.O., Ortega, E.M. and Cordeiro, G.M., (2010). The Beta Modified Weibull Distribution. Lifetime Data Analysis, 16, 409-430. [DOI:10.1007/s10985-010-9161-1]
19. Wang, F.K. (2000). A New Model with Bathtub-shaped Failure Rate Using an Additive Burr XII Distribution. Reliability Engineering and System Safety, 70, 305-312. [DOI:10.1016/S0951-8320(00)00066-1]
20. Xie, M. and Lai, C.D. (1995). Reliability Analysis Using an Additive Weibull Model with Bathtub Shaped Failure Rate Function. Reliab. Eng. Syst. Safety, 52, 87-93. [DOI:10.1016/0951-8320(95)00149-2]
21. Xie, M., Tang, Y. and Goh, T.N. (2002). A Modified Weibull Extension with Bathtub Failure Rate Function. Reliab. Eng. Syst. Safety, 76, 279-285. [DOI:10.1016/S0951-8320(02)00022-4]
Send email to the article author

Add your comments about this article
Your username or Email:

CAPTCHA

XML   Persian Abstract   Print

Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Bahrami E, Yarmoghaddam N. A New Lifetime Distribution: The Beta Modified Weibull Power Series Distribution. JSRI. 2019; 16 (1) :1-31
URL: http://jsri.srtc.ac.ir/article-1-323-en.html
Volume 16, Issue 1 (9-2019) Back to browse issues page
مجله‌ی پژوهش‌های آماری ایران (علمی - پژوهشی) Journal of Statistical Research of Iran JSRI
Persian site map - English site map - Created in 0.04 seconds with 29 queries by YEKTAWEB 4287