Generalized weibull distributions

Weibull distributions are one of the most popular continuous distributions used in survival analysis for modeling error / failure times such as deterioration and wear, early death. Nowadays, this distribution is used to determine duration of epidemic diseases in a region, to predict the magnitude of the earthquake or to compute the wind speed in a region, and to model the claim size in insurance. In other words, this distribution has become one of the most popular distributions among distributions, since the random variable can be used if the variable takes positive values. Although the Weibull distribution is frequently used in reliability and survival analysis, it is seen that this distribution is insufficient in data modeling due to its non-monotonic hazard function shape such as bathtub function or unimodal. This situation revealed that the Weibull distribution should be more flexible in data modeling. This requirement has increased the studies on obtaining new probability distributions by expanding the known distributions. When the previous studies are examined, new Weibull distributions are obtained by methods such as exponentiation, transformation (linear, inverse, logarithmic) and parameter addition. In this study, Weibull distributions in the literature are introduced at first. Later, a new generalized Weibull distribution was derived using the generalized Topp-Leone distribution family proposed by Salman et al. (2019). Hazard function and structure, moment characteristics, parameter estimation, entropy and order statistics related to this distribution, which is named as generalized Topp-Leone Weibull distribution, were obtained. The proposed distribution was shown to be more flexible than the distributions in the literatüre via an application study.