Non Central Moments of the Truncated Normal Variable

Abstract

This paper computes the non central moments of the Truncated Normal variable, that is, a Normal variable constrained to assume values in the interval with extremes that can be finite or infinite.

We define two recursive expressions where one can be expressed in closed form. Another closed form is defined using the Lower Incomplete Gamma Function.

Moreover, an upper bound for the absolute value of the non central moments is determined.

The numerical results of the expressions are compared and the different behavior for high value of the order of the moments is shown.

Keywords: truncated normal variable, non central moments, lower incomplete gamma function

JEL Classification: G11, G14, G24