A Coherent Framework for Semicontinuous Data Through Distributional Regularization, Censoring, and Compounded Occurrence-Severity Modeling

Abstract

Semicontinuous outcomes frequently present severe distributional mismatches characterized by structural zeros, highly skewed positive observations, and extreme right tails. In practice, transformations, capping, truncation, and censoring are commonly employed to reduce the influence of extreme observations. However, estimation procedures often continue to treat the modified responses as exact observations, creating a mismatch between the information contained in the data and the likelihood being optimized. We propose a coherent framework for semicontinuous long-tailed data that integrates compounded occurrence-severity modeling, power transformation, and right-censored likelihood estimation within a unified likelihood-based structure. The framework isolates the underlying causes of distributional mismatch by separately addressing structural zero mass, empirical skewness, and extreme-tail boundary behavior while preserving the compounded relationship between occurrence probability and conditional severity. A closed-form deviance, gradient vector, and Hessian matrix are derived, enabling efficient likelihood-based estimation and machine-learning implementation. The proposed methodology provides a statistically coherent approach for correcting distributional mismatches in semicontinuous outcomes in applications where transformation and censoring are routinely employed.