A New Family of Continuous Probability Distribution: Gamma-Exponential Distribution (GED)Theory and its Properties

While probability distribution functions are crucial for simulating random processes, research on these functions and their features is required. However, studies have demonstrated that in certain cases, it is discovered that certain combinations of two or more random variables with known probability distributions follow the distributions of certain real-world data that cannot be sufficiently represented by the standard distributions now in use.In order to generate a new distribution combining the gamma and exponential distributions, this research work focused on creating the two-parameter Gamma-Exponential Distribution (GED), which was obtained by using the Transformed-Transformer method. Its properties included the following: expressions for its survival function and hazard function, as well as the probability density function, cumulative distribution function, rth non-central moments, first four moments, variances, skewness and kurtosis, and maximum likelihood estimator.