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Are there too many uncited articles? Zero inflated variants of the discretised lognormal and hooked power law distributions© 2016 Elsevier Ltd. Although statistical models fit many citation data sets reasonably well with the best fitting models being the hooked power law and discretised lognormal distribution, the fits are rarely close. One possible reason is that there might be more uncited articles than would be predicted by any model if some articles are inherently uncitable. Using data from 23 different Scopus categories, this article tests the assumption that removing a proportion of uncited articles from a citation dataset allows statistical distributions to have much closer fits. It also introduces two new models, zero inflated discretised lognormal distribution and the zero inflated hooked power law distribution and algorithms to fit them. In all 23 cases, the zero inflated version of the discretised lognormal distribution was an improvement on the standard version and in 16 out of 23 cases the zero inflated version of the hooked power law was an improvement on the standard version. Without zero inflation the discretised lognormal models fit the data better than the hooked power law distribution 6 out of 23 times and with it, the discretised lognormal models fit the data better than the hooked power law distribution 9 out of 23 times. Apparently uncitable articles seem to occur due to the presence of academic-related magazines in Scopus categories. In conclusion, future citation analysis and research indicators should take into account uncitable articles, and the best fitting distribution for sets of citation counts from a single subject and year is either the zero inflated discretised lognormal or zero inflated hooked power law.