Theoretical Aspects for Bayesian Predictions Based on Three-Parameter Burr-XII Distribution and Its Applications in Climatic Data

Abstract

Symmetry and asymmetry play vital roles in prediction. Symmetrical data, which follows a predictable pattern, is easier to predict compared to asymmetrical data, which lacks a predictable pattern. Symmetry helps identify patterns within data that can be utilized in predictive models, while asymmetry aids in identifying outliers or anomalies that should be considered in the predictive model. Among the various factors associated with storms and their impact on surface temperatures, wind speed stands out as a significant factor. This paper focuses on predicting wind speed by utilizing unified hybrid censoring data from the three-parameter Burr-XII distribution. Bayesian prediction bounds for future observations are obtained using both one-sample and two-sample prediction techniques. As explicit expressions for Bayesian predictions of one and two samples are unavailable, we propose the use of the Gibbs sampling process in the Markov chain Monte Carlo framework to obtain estimated predictive distributions. Furthermore, we present a climatic data application to demonstrate the developed uncertainty procedures. Additionally, a simulation research is carried out to examine and contrast the effectiveness of the suggested methods. The results reveal that the Bayes estimates for the parameters outperformed the Maximum likelihood estimators.