Persistence is the most important property in any hydrologic design concerning the storage capacity of reservoirs, average return periods, failure risks, and drought properties. Its consideration in analytical derivations of design criteria presents difficulties, especially in autocorrelated hydrologic processes, and for this reason, most often the analytical expressions are obtained on the basis of non-persistent (independent) cases. Although the conventional autocorrelation coefficients and function are used in many hydrological design problems, the very definition of the autocorrelation function requires that the underlying hydrologic process generating mechanism abide with normal (Gaussian) probability distribution function in addition to other restrictive assumptions. Since almost all of the analytical stochastic approaches are based on the normality assumption, it is necessary to transform non-Gaussian distributions to the normal distribution to use analytical expressions. During the transformation process, the very genuine persistence property of the basic hydrologic variables is not preserved, even when the statistical parameters such as the average, standard deviation, skewness coefficient, kurtosis, etc., are maintained in the transformed data. This shortcoming in the autocorrelation function is by-passed by the introduction and use of an autorun function, which is probability distribution free and a robust parameter. Its basis is the conditional probability statement which does not require any assumptions in practical applications. Various practical and simple hydrological design quantities are developed on the basis of the autorun coefficients without considering the conventional autocorrelation structure. The application of methodology is presented for John's river in Florida.