UC Santa Barbara

ABSTRACT: Truncated samples arise in a variety of hydrologic situations in which certain values of the variables of interest are unobservable. Remotely sensed data, for example, are truncated below the resolution level of the sensor: all objects smaller than the resolution of the instrument are not detected and their characteristics cannot be recorded. Many other situations occur in hydrologic studies where a sampling procedure or method yields truncated samples. The main results on this work on truncated samples are: (1) a general expression for the probability distribution function of a truncated random variable; (2) a description of the effect of truncation on the distribution function of several important probability models and on their parameters; and (3) development of a parameter estimation methodology for parameter estimation from truncated samples. From the theoretical results of this paper and the analysis of drought‐related data, we have concluded that: (1) truncated sampling can be advantageous, especially when certain ranges of values are difficult or impossible to observe; (2) the developed method for truncated sample analysis leads to efficient and accurate parameter estimation and statistical inference on truncated data; and (3) the developed method for truncated sample analysis can also yield the parameters and the distribution of the entire population when only a subset of that population is observable. Copyright © 1992, Wiley Blackwell. All rights reserved