Weighted Simultaneous Tolerance Intervals and Multiple-Use Univariate Calibration based on Combination Information
Description
Research Hypothesis: this study assumes that the random error terms of the univariate linear correction model based on combined information follow a normal distribution, and the variances of random error terms are different across data sources of distinct dependent variables. Data Collection: since this study focuses on model performance validation, all analytical data were randomly simulated in R with preset parameters of the Beta distribution. The data generation procedure strictly complied with the research hypotheses to construct the final analytical dataset. Both data generation and statistical computation were implemented via R programming. Main Findings: numerical simulations on the generated datasets indicate that the proposed confidence intervals satisfy the coverage probability requirements. Moreover, when the intervals of covariates are relatively narrow, the proposed method presents a prominent advantage in average interval length under both skewed and symmetric distributions. Data Interpretation and Usage: the research results can be interpreted in combination with figures, tables and textual explanations in this paper. The rules for data collection and data processing procedures are fully documented. The dataset can be used for comparative analysis, model construction and empirical research by other researchers, and all analytical procedures are fully reproducible under identical conditions.