On the comparison of variances of <i>X</i> and <i> X _T </i> , hidden truncated version of <i>X</i> : a brief study

Hidden truncation (alias latent variable) models play an important role in modeling various types of observed phenomena when one or more than one concomitant variable(s) is/are truncated below/ above or from both sides (alias two-sided) from a threshold value (depends on the support set and the model parameter(s)of the conditioning variable) that is often guided by the practitioner working in this field. Although probabilistic behavior, structural properties, and the inferential aspects associated with such types of models have been well discussed in the literature, not much discussion has been made on the equality/inequality between the variance of a truncated version of a random variable with that of it’s non-truncated version. In this article, some ideas are presented with illustrative examples to address this issue.