IN THIS PAPER, WE PRESENT THE UNIT-POWER HALF-NORMAL DISTRIBUTION, DERIVED FROM THE POWER HALF-NORMAL DISTRIBUTION, FOR DATA ANALYSIS IN THE OPEN UNIT INTERVAL. THE STATISTICAL PROPERTIES OF THE UNIT-POWER HALF-NORMAL MODEL ARE DESCRIBED IN DETAIL. SIMULATION STUDIES ARE CARRIED OUT TO EVALUATE THE PERFORMANCE OF THE PARAMETER ESTIMATORS. ADDITIONALLY, WE IMPLEMENT THE QUANTILE REGRESSION FOR THIS MODEL, WHICH IS APPLIED TO TWO REAL HEALTHCARE DATA SETS. OUR FINDINGS SUGGEST THAT THE UNIT POWER HALF-NORMAL DISTRIBUTION PROVIDES A ROBUST AND FLEXIBLE ALTERNATIVE FOR EXISTING MODELS FOR PROPORTION DATA.