$$\boldsymbol{S}$$-Distribution, a New One-Parameter Exponential-Gamma Distribution: Properties and Applications

A new one-parameter exponential-gamma distribution called the $$S$$ -distribution is proposed in this study. Various mathematical and statistical properties of the new distribution are presented. The likelihood estimation method using an iterative algorithm is used to estimate the distribution’s parameter. The new proposition is assessed using different real lifetime data. Its performance is compared with other one-parameter exponential-gamma distributions and some generic two-parameter distributions. Using different selection criteria, results from the application show that the new proposed distribution provides better fit to the data.