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A Novel Generalized-M Family: Heavy-Tailed Characteristics with Applications in the Engineering Sector

The Weibull distribution has prominent applications in the engineering sector. However, due to its monotonic behavior of the hazard function, the Weibull model does not provide the best fit for data in many cases. This paper introduces a new family of distributions to obtain new flexible distributions. The proposed family is called a novel generalized-
 
 M
 
 family. Based on this approach, an updated version of the Weibull distribution is introduced. The updated version of the Weibull distribution is called a novel generalized Weibull distribution. The proposed distribution is able to capture four different patterns of the hazard function. Some mathematical properties of the proposed method are obtained. Furthermore, the maximum likelihood estimators of the proposed family are also obtained. Moreover, a simulation study is conducted for evaluating these estimators. For illustrating the proposed model, two data sets from the engineering sector are analyzed. Based on some well-known analytical measures, it is shown that the novel generalized Weibull distribution is the best competing distribution for analyzing the engineering data sets.