A novel logarithmic approach to generate new probability distributions for data modeling in the engineering sector

In this paper, we introduce a new statistical methodology for updating the flexibility level
of the traditional distributions. The newly developed method is called, the logarithmic-U family of
distributions. For the logarithmic-U distributions, the estimation of the parameters via the maximum likelihood method is discussed. Some mathematical properties of the logarithmic-U distributions are also derived. By using the logarithmic-U method, an updated version of the Weibull
model, namely, the logarithmic Weibull distribution is introduced. A simulation study for the
logarithmic Weibull distribution is provided. Finally, the practical illustration of the logarithmic
Weibull distribution is shown by analyzing two data sets taken from the engineering sector. The first
data set represents the fracture toughness of Al2O3 material. Whereas, the second data set represents the fatigue fracture of Kelvar 373/epoxy. The practical applications show that the proposed logarithmic Weibull distribution is very competent for analyzing data sets in engineering and
other related sectors.