Bayesian Prediction of Network Latency Times Under Maximum-Type Gumbel Current Records

Accurate modeling and prediction of extreme network latency are essential for evaluating communication performance and reliability. This study develops a comprehensive inferential and predictive framework for upper and lower current records when the underlying observations follow the maximum-type Gumbel (MtG) distribution. The main theoretical contributions include deriving the probability density functions (PDFs) and cumulative distribution functions (CDFs) of both types of current records, obtaining integral representations of their moments, and establishing conditional distributions for future record observations. Maximum likelihood and Bayesian methods are employed to estimate the location and scale parameters, with Bayesian inference implemented numerically using the Metropolis–Hastings algorithm. Furthermore, classical prediction intervals and Bayesian predictive values and intervals are developed for future upper and lower current records and their corresponding ranges. A Monte Carlo simulation study evaluates the estimation procedures in terms of their statistical performance, while an application to the weekly network latency measurements from Saudi Arabia demonstrate the practical applicability of the proposed methodology. The results illustrate how the proposed framework characterizes record-high and record-low latency values and quantifies the uncertainty associated with future extreme observations. From a practical perspective, the methodology provides statistical tools for monitoring unusual network delays, anticipating extreme latency behavior, and supporting informed decisions concerning network performance and reliability.