In actuarial studies, insurance losses are treated as random variables, and researchers seek appropriate probabilistic models
 to represent them. Since losses are evaluated in terms of a unity amount, distributions with positive support are typically used
 to model them. While this poses no issue for univariate cases, it becomes more complicated in multivariate scenarios. While
 copulas can be helpful in such situations, studying correlation is a crucial initial step. The Pearson correlation coefficient,
 widely used in statistical analysis, measures the strength and direction of the linear relationship between two variables.
 Furthermore, we analyze a real-world dataset from an Iranian insurance company, including losses due to physical damage
 and bodily injury, as covered by third-party liability insurance. Upper and lower limits for both the Pearson correlation
 coefficient and its estimator were derived from the analysis. Furthermore, two methodswereusedtodeterminethecorrelation
 between physical damage and bodily injury, and then the results were compared. Instead, our analysis reveals that narrower
 bounds can be established for the Pearson correlation coefficient in such cases. The results of this study provide important
 insights into modeling insurance losses in multivariate cases and have practical implications for risk management and pricing
 decisions in the insurance industry.