Forecasting temperature data for two counties in California using the stress–strength reliability of the MO q-GEVL distribution: A return level based approach and time series

In this article, the stress–strength reliability ( S S R = P ( X < Y ) ), where both stress X and strength Y follow a new model called Marshall Olkin’s q extended generalized extreme value linear distribution ( M - q GEVL ) under type II progressive censoring, is investigated. The S S R estimation is considered using both maximum likelihood estimation ( M L E ) and Bayesian estimation ( B E ). Since the M L E equations are extremely complex, a metaheuristic optimization technique called the Whale Optimization Algorithm (WOA) is utilized. The B E is considered for both informative and non informative cases using both Linex and square error loss functions. Temperature data from Sacramento and Los Angeles counties in California are also used to demonstrate the proposed statistical methodology, showing that the M - q G E V L model provides a better fit than both q G E V L and G E V L based on lower S K , A I C , and B I C values. Time series analysis, return level, and S S R are applied to predict future temperatures, and the results consistently indicate higher predicted temperatures in Los Angeles than in Sacramento.