The objective of this paper is to explain the distributions, assumptions, interpretations, and relationships of the two compatible, stochastic models of fire history: the negative exponential and the Weibull. For each model the 'fire interval' and 'time-since-fire' distributions are given. Both models apply to homogenous stationary stochastic processes. The negative exponential states that the instantaneous fire hazard rate is constant for all stand ages. The Weibull states that the instantaneous fire hazard rate increases with stand age when the shape parameter is > 1 (the negative exponential is a special case of the Weibull when shape = 1). An empirical method is given for separating from an observed fire history distribution, the pre- and post-fire suppression distributions. Four relationships are derived from the models and defined per study region (per stand): (i) the fire cycle (average fire interval), (ii) the annual percent burned area (fire frequency), (iii) the average age of the vegetation (average prospective life-time), and (iv) the renewal rate.