Abstract
The existence of orthogonal parameters to the mean is characterized by a partial differential equation involving the mean, the variance and the cumulant generating function. This condition allows to explain and construct orthogonal parametrizations in several cases of interest, including higher parametric ones.
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Hürlimann, W. On parameter orthogonality to the mean. Statistical Papers 33, 69–74 (1992). https://doi.org/10.1007/BF02925313
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DOI: https://doi.org/10.1007/BF02925313