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This paper proposes the singly truncated normal distribution as a model for estimating radiance measurements from satellite-borne infrared sensors. These measurements are made in order to estimate sea-surface temperatures which can be related to radiances. Maximum-likelihood estimation is used to provide estimates for the unknown parameters. In particular, a procedure is described for estimating clear radiances in the presence of clouds and the Kolmogorov-Smirnov statistic is used to test goodness-of-fit of the measurements to the singly truncated normal distribution. Tables of quantile values of the Kolmogorov-Smirnov statistic for several values of the truncation point are generated from Monte Carlo experiments. Finally a numerical example using satellite data is presented to illustrate the application of the procedures.