General expressions are derived for the distribution functions of the total amount of precipitation and the largest daily precipitation occurring in an n-day period. Two special cases are considered: (i) the probability of occurrence of precipitation on any day in an n-day period is a constant (binomial counting process) and (ii) the probability of occurrence of precipitation on any day depends on whether the previous day was wet or dry (Markov chain counting process). The distribution function for daily precipitation was assumed to be exponential. Analytic expressions are derived for the distribution functions for total precipitation or precipitation greater than a threshold. For the numerical example chosen, the Markov chain-exponential model is slightly superior to the binomial-exponential model. This stochastic model seems to have several advantages over present approaches. Abstract General expressions are derived for the distribution functions of the total amount of precipitation and the largest daily precipitation occurring in an n-day period. Two special cases are considered: (i) the probability of occurrence of precipitation on any day in an n-day period is a constant (binomial counting process) and (ii) the probability of occurrence of precipitation on any day depends on whether the previous day was wet or dry (Markov chain counting process). The distribution function for daily precipitation was assumed to be exponential. Analytic expressions are derived for the distribution functions for total precipitation or precipitation greater than a threshold. For the numerical example chosen, the Markov chain-exponential model is slightly superior to the binomial-exponential model. This stochastic model seems to have several advantages over present approaches.