A Note on the Sum of Non-Identically Distributed Doubly Truncated Normal Distributions

TL;DR

This paper proves that the sum of independent, non-identically distributed doubly truncated Normal variables converges to a Normal distribution and discusses its application in constrained mixed effects model estimation.

Contribution

It establishes a convergence result for sums of non-identically distributed doubly truncated Normal variables and demonstrates its use in estimating constrained mixed effects models.

Findings

Sum of such variables converges to Normal distribution

Provides a method for applying this result in mixed effects models

Enhances understanding of truncated Normal sum behavior

Abstract

It is proved that the sum of n independent but non-identically distributed doubly truncated Normal distributions converges in distribution to a Normal distribution. It is also shown how the result can be applied in estimating a constrained mixed effects model.