Rayleigh Current Record Distributed Data: Estimation and Prediction with Application on Saudi Arabia Industrial Data

Abstract In this paper, we tried to analyze current record data when the primary data already follows the Rayleigh distribution. The current record is a method that works somewhat like the usual record (upper and lower), but in this case, we store them together each time one of them is updated, and do not change the other. By subtracting them in each step, we obtain the record range. We will find some closed forms for the cumulative distribution functions (CDFs) of the upper current record and the lower current record, along with their probability density functions (PDFs). Additionally, some easily calculated formulas for both types will be introduced, along with an estimate for the new proposed distribution’s parameters. A prediction algorithm will be developed to enhance the applicability of the prediction process. Finally, two examples will be used to demonstrate the valuable application of the paper’s findings: one is a simulation study, and the other is a real-life dataset from Saudi Arabia’s industrial sector.