Unified and non-recursive formulas for moments of the normal distribution with stripe truncation

Haruhiko Ogasawara

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 19, 6834-6862

Abstract: Stripe truncation in the normal distribution is introduced such that the variable is truncated when it is located on several intervals like stripes. This truncation includes single, double and elliptical truncation as special cases. Then, the moments and absolute moments of arbitrary orders for the deviation of the truncated variable from an arbitrary reference point are derived using closed-form formulas based on the incomplete gamma function. The corresponding absolute moments of non-integer valued orders are also derived employing the parabolic cylinder distribution. The formulas do not suffer from difficulties associated with the conventional recursive methods for higher-order moments.

Date: 2022
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DOI: 10.1080/03610926.2020.1867742

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