The correlation between two hydrology randon variables with arbitrary distribution functon is distinguished. The characteristics of correlation between two hydrology randon variables with the normal distribution function are analysed. Thefundamentals of Copula function and deformation function ditermined binarry distribution runction between two hydrology randon variables are discussed. The natures of Copula function method and deformation function method are pointed out. Finally, applications of binary distributon function in in terpolation and extension of data, probability hydrology forecasting, frequency analysis of inconsistency sample, risk probability of water engineering, design flood, geomorphologic instantameous unit hydrograph etc. are dissected and prospected.