Rainfall is the main input for probabilistic analysis and prediction of rainfall-triggered landslide. The joint probabilistic structure of daily rainfall (DR) and cumulative rainfall (CR)

which are dominant parameters of rainfall related on landslide in Chongqing region

was analyzed. Following the traditional technology

daily rainfall was translated into discrete variable by rainfall grade and cumulative rainfall became continuous variable if records with very small cumulative rainfall were ignored. Then joint probabilistic model of discrete variable and continuous one was derived

and transiting solution of conditional density function was put forward

together with its approximation via a family of Dirac δ sequences. Naturally

the proposed method was used to analyze conditional density function of cumulative rainfall in Chongqing region

and the numerical results were verified by comparison. However

most of the conditional density functions were irregular and not modeled by simple probability density function

thus the finite mixture distribution was introduced

which is of uncomplicated format and relatively high precision. At last

the joint probabilistic model of daily rainfall and cumulative rainfall was built up by combining frequency function of grade of daily rainfall with conditional density model of cumulative rainfall.