First moments of the truncated and absolute Student's variates

TL;DR

This paper derives the first two moments of truncated and absolute Student's t-distributed variables, providing analytical results for these modified distributions.

Contribution

It offers new analytical expressions for the moments of truncated and folded Student's t-distributions, extending existing knowledge.

Findings

Derived the first two moments of truncated Student's t-distribution.

Derived the first two moments of absolute (folded) Student's t-distribution.

Results facilitate statistical analysis involving truncated or folded t-distributions.

Abstract

While some of the enclosed already is a well-known derivation, and the remaining may have been obtained in earlier publications, this note computes the first two moments of a Student's variate truncated at zero and of an absolute (or folded) Student's variate.