Extended truncated Inverse Gaussian—Poisson model

摘要

The inverse Gaussian—Poisson mixture model is very useful when modelling highly skewednon-negative integer data in fields as diverse as linguistics, ecology, market research, bibliometry, engi-neering and insurance. When using this statistical model on the frequency of word or species frequencydata, one typically truncates its sample space at zero to accommodate for the ignorance about thenumber of words or species that are not observed. In this paper, we show that by truncating the samplespace of the inverse Gaussian—Poisson model, one is allowed to extend its parameter space and in thatway improve its fit when the frequency of one is larger and the right tail is heavier than is allowed bythe unextended model. By fitting the extended model to word frequency count data, we find manyinstances where the maximum likelihood estimates fall in the extension of the parameter space.