[en] A method is developed for deriving a set of equations relating the public risk in potential nuclear reactor accidents to the basic variables, such as population distributions and radioactive releases, which determine the consequences of the accidents. The equations can be used to determine the risk for different values of the basic variables without the need of complex computer programs and can be used to determine the variable values which are needed to satisfy various risk criteria. The methodology developed in this study consists of two steps. The first step involves fitting the risk distributions of frequency versus consequence to parametric distributions which contain a small number of parameters. The second step involves deriving the equations which relate the distribution parameters to the basic variables of interest. Regression techniques are used for this second step. The methodology is demonstrated for examples based on the results of the Reactor Safety Study. The calculated distributions of early fatalities in nuclear reactor accidents and the historical records of fatalities in hurricanes, tornadoes, earthquakes and dam failures are examined to determine an appropriate family of parametric distributions. From these examinations, the Weibull distribution is found to be appropriate for all of the examined events. A set of equations is then derived which relate the population distribution and the parameters of the Weibull distributions for early fatalities from PWR accidents. Regression equations relating the parameters to the characteristics of radioactive releases are also derived