Exceedances and Moments in Data Containing Zeros

Abstract

Rain rate-the speed of rain in mm/hr-assumes zero values when it is not raining, and positive values on a continuum otherwise. For large areas, empirical evidence points to a high correlation between the instantaneous area average rain rate and the instantaneous fractional area where rain rate exceeds a fixed positive threshold. An explanation is provided by appealing to the man value theorem for integrals, in conjunction with the mixed nature of the probability distribution of rain rate. Using a multinomial logits model, the fractional area also is shown useful as a time dependent covariate in categorical prediction of the area average.