Moment Generating Function of Current Records Based on Generalized Exponential Distribution with Some Recurrence Relations

This paper tries to find some formulas for calculating the moment generating function for upper and lower current records picked from generalized exponential distributed data and the joint moment generating function between them. After that, some formulas are derived from the previous ones to find the moments of each and the product moments of both upper and lower current records. Then, various recurrence relations are established for most of the mentioned formulas. After that, an integral form of the moments of record range is founded followed by a numerical example with simulated data to clarify the effectiveness of the formulas found in the study and how they can make the calculation process easier and faster. Finally, a conclusion part is added, to sum up what has been done and the results.