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The Sectionally Truncated Normal Distribution

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Expository Moments for Pseudo Distributions

Part of the book series: Behaviormetrics: Quantitative Approaches to Human Behavior ((BQAHB,volume 2))

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Abstract

Sectional truncation introduced by Ogasawara (J Multivar Anal [32]) is the multivariate version of stripe (tigerish) truncation proposed by Ogasawara (Commun Stat Theor Methods [31]) including usual single and double truncation as special cases. The partial derivatives of the cumulative distribution function of the normally distributed vector are derived. Using these results and the moment generating function for the normal vector under sectional truncation, moments and cumulants of the distribution are obtained. As an associated result of the Hermite polynomials found in the derivation, the product sum of natural numbers is introduced with its properties.

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Authors and Affiliations

  1. Professor Emeritus, Otaru University of Commerce, Otaru, Hokkaido, Japan

    Haruhiko Ogasawara

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  1. Haruhiko Ogasawara
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Correspondence to Haruhiko Ogasawara .

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Ogasawara, H. (2022). The Sectionally Truncated Normal Distribution. In: Expository Moments for Pseudo Distributions. Behaviormetrics: Quantitative Approaches to Human Behavior, vol 2. Springer, Singapore. https://doi.org/10.1007/978-981-19-3525-1_1

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