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.

摘要

引入了正态分布中的条截断，这样，当变量位于像条一样的几个间隔时，变量就会被截断。作为特殊情况，此截断包括单，双和椭圆截断。然后，基于不完整的伽马函数，使用封闭式公式得出截断变量与任意参考点的偏差的任意阶矩和绝对矩。还使用抛物柱面分布推导了非整数值阶的相应绝对矩。对于高阶矩，这些公式不会遇到与常规递归方法相关的困难。