A versatile family of distributions: Log-linear regression model and applications to real data

This article introduces a tractable generator for constructing flexible families of continuous distributions called the exponent-G-M (ExpG-M). Properties of the defined models generator are studied such as moments, mean deviation, moment of residual life, entropy, and order statistics. The ExpG-M model’s parameter was estimated using both maximum likelihood estimation (MLE) and Bayesian estimation (BE) methods with a square error loss function, also assessed through Monte Carlo simulation studies. A special member called exponent generalized exponential-exponential distribution (ExpGE-E) is discussed; a related log-regression model based on ExpGE-E is introduced. Applications of the ExpGE-E and its regression model to real-life datasets shows that the proposed models have better modeling abilities than many competing distributions.