Testing parametric distribution family assumptions via Difference in Differential Entropy

The choice of an appropriate parametric distribution family is fundamental for valid statistical inference and empirical modeling. However, economic theory often provides limited guidance regarding the correct functional form governing the data-generating process. The new Difference in Differential Entropy (DDE) test is an information-theoretic statistical procedure for testing composite distributional hypotheses. The test provides a unified framework applicable across a broad class of parametric families of distributions and is grounded in established principles of maximum likelihood estimation, kernel density estimation, and parametric bootstrap inference. The procedure compares a parametric maximum likelihood estimate of differential entropy under the null hypothesis with a nonparametric kernel-density-based estimate constructed from the sample data. Their divergence serves as a goodness-of-fit measure for evaluating the validity of the hypothesized distribution family. The method is computationally tractable, straightforward to implement, and does not require distribution-specific asymptotic derivations or complex tuning procedures. Monte Carlo experiments demonstrate favorable size and power properties, including in relatively small samples. Comparisons with the classical Kolmogorov–Smirnov and Anderson–Darling procedures indicate that the DDE test performs competitively across a broad range of alternatives and offers some distinct advantages. Empirical applications using classical datasets illustrate the practical usefulness and flexibility of the proposed test.