An Empirical Assessment of the Closeness of Hidden Truncation and Additive Component based Skewed Distributions

Hidden truncation (HT) and additive component (AC) are two well known paradigms of generating skewed distributions from known symmetric distribution. In case of normal distribution it has been known that both the above paradigms lead to Azzalini’s (1985) skew normal distribution. While the HT directly gives the Azzalini’s (1985) skew normal distribution, the one generated by AC also leads to the same distribution under a re-parameterization proposed by Arnold and Gomez (2009). But no such re-parameterization which leads to exactly the same distribution by these two paradigms has so far been suggested for the skewed distributions generated from symmetric logistic and Laplace distributions. In this article, an attempt has been made to investigate numerically as well as statistically the closeness of skew distributions generated by HT and AC methods under the same re-parameterization of Arnold and Gomez (2009) in the case of logistic and Laplace distributions.