The analysis of word frequency count data can be very useful in authorship attribution problems. Zerotruncatedgeneralized inverse Gaussian–Poisson mixture models are very helpful in the analysis of thesekinds of data because their model-mixing density estimates can be used as estimates of the density of theword frequencies of the vocabulary. It is found that this model provides excellent fits for theword frequencycounts of very long texts, where the truncated inverse Gaussian–Poisson special case fails because it doesnot allow for the large degree of over-dispersion in the data. The role played by the three parameters ofthis truncated GIG-Poisson model is also explored. Our second goal is to compare the fit of the truncatedGIG-Poisson mixture model with the fit of the model that results from switching the order of the mixingand truncation stages. A heuristic interpretation of the mixing distribution estimates obtained under thisalternative GIG-truncated Poisson mixture model is also provided.