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On a new extension of Weibull distribution: Properties, estimation, and applications to one and two causes of failures
Author(s) -
Nassar Mazen,
Afify Ahmed Z.,
Shakhatreh Mohammed K.,
Dey Sanku
Publication year - 2020
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2671
Subject(s) - frequentist inference , weibull distribution , estimator , mathematics , logarithm , extension (predicate logic) , computer science , statistics , bayesian probability , bayesian inference , mathematical analysis , programming language
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.