A New Truncated Muth Generated Family of Distributions with Applications

In recent years, the Muth distribution has been used for the construction of accurate statistical models, with applications in various applied fields. In this paper, we use a truncated‐composed scheme to create a new unit Muth distribution, from which we motivate a more general family of continuous distributions called the truncated Muth generated family. The key benefits of this family are its analytical simplicity, connections with the exponential generated family, and flexibility conferred on any parental distribution. In particular, it improves the capability of the functions of the parental distribution, enhancing their peak, asymmetry, tail, and flatness levels, among others. The characteristics of quantile and moment measures and functions of the truncated Muth generated family are described in detail. As a concrete example, a particular distribution that extends the Weibull distribution is highlighted. In an applied part, the parameters are calculated using the maximum likelihood procedure. We use a comprehensive simulation analysis to demonstrate the accuracy of the derived estimates. The revised Weibull model is then used to fit two real‐world datasets. The new model is shown to be more suited to these datasets than other competing models.