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Symmetrical as well as asymmetrical statistical models play a prominent role in describing and predicting the real-world phenomena of nature. Among other fields, these models are very useful for modeling data in the sector of civil engineering. Due to the applicability of the statistical models in civil engineering and other related sectors, this paper offers a statistical methodology to improve the distributional flexibility of traditional models. The suggested method/approach is called the extended-X family of distributions. The proposed method has the ability to generate symmetrical and asymmetrical probability distributions. Based on the extended-X family approach, an updated version of the Weibull model, namely, the extended Weibull model, is studied. The proposed model is very flexible and has the ability to capture the symmetrical and asymmetrical shapes of its density function. For the extended-X method, the estimation of parameters, a simulation study, and some mathematical properties are derived. Finally, the practical illustration/usefulness of the suggested model is shown by analyzing two data sets taken from the field of engineering. Both data sets represent the fracture toughness of alumina (Al2O3).

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.

This paper proposes a PLS Model for the study of Online Trading. Traditional investing has experienced a revolution due to the rise of e-trading services that enable investors to use Internet conduct secure trading. On the hand, model results show that there is a positive, direct and statistically significant relationship between personal outcome expectations, perceived relative advantage, shared vision and economy-based trust with the quality of knowledge. On the other hand, trading frequency and portfolio performance has also this relationship. After including the investor’s income and financial wealth (IFW) as moderating effect, the PLS model was enhanced, and we found that the interaction term is negative and statistically significant, so, higher IFW levels entail a weaker relationship between trading frequency and portfolio performance and vice-versa. Finally, with regard to the goodness of overall model fit measures, they showed that the model is fit for SRMR and dG measures, so it is likely that the model is true.