Abstract
The offset normal distribution, defined as the induced shape parameter of a Gaussian random configuration in the plane, is one of the most important probability distributions with tremendous applications both in pure and applied mathematics. In this paper some basic properties of the offset normal distribution are discussed. Based on the basic properties, several characterizations are presented by the left and right truncated moments. The first characterization result is based on a relation between left truncated moment and failure rate function. The second characterization result is based on a relation between right truncated moment and reversed failure rate function.
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