The article explores different types of G-family distributions like Kumaraswamy-G, Zografos-Balakrishnan-G, and Ristic-Balakrishnan-G. The researchers investigate the mathematical properties of these distributions and discover new ones based on them. They analyze the Zografos-Balakrishnan-generalized exponential distribution, including its probability density function, cumulative distribution function, hazard rate function, moments, quantile function, entropy, and parameter estimation using maximum likelihood method.