A Characterization Theorem Based on Truncated Moments and its Application to Some Distribution Families
A new representation theorem for distributions of real-valued random variables is presented. The theorem is based on a relationship between different truncated moments of the same random variable. As an example of its application, characterization theorems for some families of both continuous and discrete distributions are derived. Further applications can be obtained after certain transformations. These characterizations may also serve as a basis for parameter estimation.
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