On a new extension of Weibull distribution: Properties, estimation, and applications to one and two causes of failures. (8th July 2020)

• Record Type: Journal Article
• Authors: Nassar, Mazen; Afify, Ahmed Z.; Shakhatreh, Mohammed K.; Dey, Sanku
• Is Part Of: Quality and reliability engineering international. Volume 36:Number 6(2020)
• Page Start: 2019
• Page End: 2043
• Publication Date: 2020-07-08
• Subjects: competing risks data -- hazard rate function -- logarithmic transformed method -- maximum likelihood estimation -- survival function; Reliability (Engineering) -- Periodicals; Quality control -- Periodicals; High technology -- Periodicals; 620.00452
• DOI: 10.1002/qre.2671
• Languages: English
• ISSNs: 0748-8017

Abstract

Abstract: In this paper, we try to supplement the distribution theory literature by introducing a new distribution, called the logarithmic transformed Weibull (LTW) distribution by logarithm transformation method. The proposed distribution exhibits constant, decreasing, increasing, unimodal and unimodal then bathtub‐shaped hazard rates. Although our main focus is on the estimation from the frequentist point of view, in addition, we derive some useful structural and statistical properties of the proposed LTW distribution. The LTW parameters are estimated by eight frequentist methods of estimation. We perform extensive simulation experiments to show the performances of the proposed estimators. Applications of the model are presented by reanalyzing two real data sets, and comparisons are made with the fit attained by some other well‐known distributions for illustrative purposes. As an illustration, one data set is analyzed for competing risks to demonstrate the flexibility of the proposed model.