Transformations for Semi-Continuous Data

Abstract

Semi-continuous data arise in many applications where naturally-continuous data become contaminated by the data generating mechanism. The resulting data contain several values that are ''too frequent'', and in that sense are a hybrid between discrete and continuous data. The main problem is that standard statistical methods, which are geared towards continuous or discrete data, cannot be applied adequately to semi-continuous data. We propose a new set of two transformations for semi-continuous data that ''iron out'' the too-frequent values thereby transforming the data to completely continuous. We show that the transformed data maintain the properties of the original data, but are suitable for standard analysis. The transformations and their performance are illustrated using simulated data and real auction data from the online auction site eBay.