Exponential-Gamma-Rayleigh Distribution: Theory and Properties

The use of traditional probability models to forecast real-world events is causing growing dissatisfaction among scholars. One of the motives could be the tail characteristics and goodness of fit metrics has a constraining tendency. Subsequently, there has been a significant increase in the generalisation of well-known probability distributions in recent years. The challenge is finding families versatile enough to fit both skewed and symmetric data. It is essential to understand that most generalised distributions described in the literature were developed using the generalised transformed transformer (T-X) method. This method was proposed by Alzaatreh et al. (2013). Also, Adewusi et al. (2019) showed that this generalization approach is beneficial by transforming the Exponential-Gamma distribution developed by Ogunwale et al. (2019) to a family of distribution known as the Exponential-Gamma-X. Therefore, in this study, we focused on developing a new family of continuous distributions called the Exponential-Gamma-Rayleigh distribution by transforming the newly generated continuous T-X family of distribution called the Exponential-Gamma-X distribution using the traditionally existing Rayleigh distribution as a transformer “X”. Several expressions for the new distribution’s theory and properties were explored and obtained; the maximum likelihood estimation approach was used to estimate the distributions' parameters, and finally, simulations studies were conducted to assess the asymptotic behaviour of the estimates.