Derivation of some statistics for beta exponential distribution

We propose a beta exponential distribution that is formed from the logarithm of a random variable with a beta value, as well as a thorough investigation of the distribution's mathematical characteristics. Because we dealt with the beta exponential distribution, we have a clear and understandable way to comprehend the equation and apply it to the actual problem. To do this, we gathered the questions that statisticians find interesting and studied the most significant properties and statistics related to the distribution. Future research will utilize this data to identify specific industrial flaws or inefficiencies as a function of survival. Included are system statistics, BE distributions for graphs, generation functions, moments, and Hazard functions.