Original Article

A new transformed Weibull lifetime distribution and its inferences based on the Bayes and maximum likelihood procedures

Abstract

Background & Aim: In last three decades or so, an extensive research works has appeared in the literature on the theory of statistical distributions. The Weibull distribution is a very popular model, and has been extensively used over the past decades for modelling data in reliability, engineering and biological studies. 
Methods & Materials: First, we obtain some of important statistical and reliability characteristics of the new model, and then the estimation of the parameters of proposed model is studied through two views of Bayesian and classic statistics. 
Results: We show that the new distribution has the ability to fit into complete and censored real data. In the application section, we show the superiority of the proposed model to some common statistical distributions.
Conclusion: In this paper, we have proposed a new transformed Weibull distribution, denoted by TWD. It is investigated that the new model has increasing, decreasing and bathtub shape hazard functions. We provide the comprehensive Bayesian and maximum likelihood estimation procedures for complete and right censored real observations.

1. Aarset MV. How to identify a bathtub hazard rate? IEEE Transactions on Reliability. 1987;36(1): 106-108.
2. Weibull W. A statistical theory of the strength of material. Ingeniors Vetenskaps Akademiens. Stockholm. 1939;151.
3. Gupta RD, Kundu D. A new class of weighted exponential distributions. Statistics. 2009;43: 621–634.
4. Kharazmi O. Generalized weighted Weibull distribution. J Mathemat Extens. 2016;10:89-118.
5. Calabria R, Pulcini G. Point estimation under asymmetric loss functions for left-truncated exponential samples. Common Stat-Theory Methods. 1996;25(3):585-600.
6. Meeker WQ, Escobar LA. Statistical methods for reliability data. John Wiley & Sons. 2014.p.23-89.
7. Badar MG, Priest AM. Statistical aspects of fiber and bundle strength in hybrid composites”, Progress in Science and Engineering Composites, Hayashi, T., Kawata, K. and Umekawa, S. (eds.). ICCM-IV. Tokyo. 1982:1129-1136.
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IssueVol 4 No 2 (2018) QRcode
SectionOriginal Article(s)
Keywords
Weibull distribution Bayesian estimation Censored data Reliability
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Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
1.
Kharazmi O, Mehregan H. A new transformed Weibull lifetime distribution and its inferences based on the Bayes and maximum likelihood procedures. JBE. 2018;4(2):99-112.