The link between Obesity and Hypertension is one of the most popular topics which have seen much discussion in recent decades but still difficult to be captured comprehensively and accurately. However, the distribution of BMI and blood pressure is usually fat tailed and severely tied. This paper adopts the ideas from Cai and Wang 1 by using data-driven copula selection approach with penalized likelihood to measure fat tailed correlation, and from Li et al.2 by employing Interval Censoring method to address tied data issue. Minimax Concave Penalty (MCP) is borrowed to perform the unbiased selection of Mixed copula model instead of Smoothly Clipped Absolute Deviation (SCAD), which was used in Cai and Wang1, for MCP is faster to get un-penalized solution. Interval Censoring method, inspired from survival analysis, is applied by considering ranks as intervals with upper and lower limits, and maximizing pseudo- likelihood to get point estimates. This paper describes the model and corresponding iteration algorithm. Also, a simulation to compare the proposed model (Mixed copula model via MCP with Interval Censoring method) versus existing model (Mixed copula model via SCAD with “Jitter” from R package applied to address tied data issue) in different conditions is presented. Additionally, the model is also applied to health data collected from China Health and Nutrition Survey (CHNS). Both numerical studies and real data analysis show positive results.