Frequency Estimation for Hydrological Samples with Zero Values

Abstract

This paper develops an estimation method for discontinuous distributions used for fitting hydrologic series with several zero events. Such series are observed in arid and semiarid regions, and may include monthly precipitation in dry seasons, annual low flow, etc. The study consists of a derivation of the basic equation of the frequency distribution, derivation of distribution moments and parameters, plotting positions for positive values that form a part of the series instead of the full sample as conditional distribution, and transformation of the conditional distribution parameters into those of the marginal distribution. Using monthly precipitation and annual low-flow data from China, and annual maximum peak discharge data from the United States, the suitability of the distribution and the estimation method is assessed.