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When the score function is the identity function - A tale of characterizations of the normal distribution

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  • Ley, Christophe

Abstract

The normal distribution is well-known for several results that it is the only to fulfil. Much less well-known is the fact that many of these characterizations follow from the fact that the derivative of the log-density of the normal distribution is the (negative) identity function. This a priori very simple yet surprising observation allows a deeper understanding of existing characterizations and paves the way for an immediate extension of various seemingly normal-based characterizations to a general density by replacing the (negative) identity function in these results with the derivative of that log-density.

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  • Ley, Christophe, 2023. "When the score function is the identity function - A tale of characterizations of the normal distribution," Econometrics and Statistics, Elsevier, vol. 26(C), pages 153-160.
    • Handle: RePEc:eee:ecosta:v:26:y:2023:i:c:p:153-160
    DOI: 10.1016/j.ecosta.2020.10.001
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    References listed on IDEAS

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