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Title: Some generalizations of the Henze theorem Authors:  Haruhiko Ogasawara - Otaru University of Commerce (Japan) [presenting]
Abstract: The Henze theorem gives the decomposition of the skew-normally (SN) distributed variable in truncated and untruncated independent normal variables. The pseudo normal (PN) distribution was introduced by the author using sectional truncation as an extension of the SN and the closed skew-normal (CSN), which use only single hidden or latent truncation. Under sectional truncation, it is shown that a similar decomposition holds in the PN, where the moment generating function is used for the derivation. The derivation is also the third proof of the Henze theorem, which was originally derived by analytical and probabilistic methods. It is shown that a similar decomposition holds in the cases of the normal finite/infinite mixture with the normal density weights (NN distributions).