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If the usage is distinct, this question's usage suggests the distinction is opaque. But to my understanding, the only difference is morphological inflection and not statistical.

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    $\begingroup$ I have just made them synonyms. zero-inflation was far more popular than zero-inflated, so I made the former the target (that is, the default value). $\endgroup$
    – whuber Mod
    Commented Nov 5, 2016 at 20:21
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    $\begingroup$ Wow, fast turnaround, @whuber. Could you take a look at our Current tag synonym candidates thread & see if there is anything actionable there? We still have [unbalanced] & [imbalanced], eg. $\endgroup$ Commented Nov 6, 2016 at 0:31

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Whuber's comment addresses this: the two are now synonyms.

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