Abstract: Aiming at the deficiencies in the researches about the probability distribution model for mixed forests tree measurement factors, a joint maximum entr
opy probability density function was put forward, based on the maximum entropy principle. This function had the characteristics of 1) each element of the function was linked to the maximum entropy function, and hence, could integrate the information about the probability distribution of measurement factors of main tree species in mixed forests, 2) the function had a probability expression of doubleweight, being possible to reflect the characteristics of the complex structure of mixed forests, and accurately and completely reflect the probability distribution of tree measurement factors of mixed forests based on the fully use of the information about the probability distribution of measurement factors of main tree species in mixed forests, and 3) the joint maximum entropy probability density function was succinct in structure and excellent in performance. The model was applied and tested in two sampling plots in Tianmu Mountain Nature Reserve. The fitting precision (R²=0.9655) and testing accuracy (R²=0.9772) were both high, suggesting that this model could be used as a probability distribution model for mixed forests tree measurement factors, and provided a feasible method to fully understand the comprehensive structure of mixed forests.

Key words: maximum entropy function, joint maximum entropy probability density function, tree measurement factor, mixed forest, shifting sand burial, soil evaporation, salt accumulation, water and salt distribution, saline water drip-irrigation, Taklimakan Desert.