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Based on Wikipedia's definition, I believe that statistical model refers to a certain sort of family of distributions, such as univariate Gaussian distributions in general.

Is there special statistical terminology for the result of applying specific parameters to a given model? For example, if $\mu = 5.48$ and $\sigma = 0.3$, then that's a specific Gaussian distribution. I assume it's not also called a statistical model, though it may represent an attempt to summarize or "model" (in the layperson's sense) some dataset. Intuitively it would seem to be an "instantiated model" though I'm not looking to invent my own terminology unless I have to.

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When it's necessary to draw a distinction you can say "completely specified model", or "model without unknown parameters", "model with all parameters known" & the like; when the parameters have been estimated from data, "fitted model", to emphasize that. When it's not necessary you can just say "model". That seems to do the job & agree with common usage—though according to the "Formal Definition" section of the Wikipedia article you cite a model is a collection of distributions, in these cases it would be a collection comprising one distribution.

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  • $\begingroup$ Thanks Scortchi. Consistent with your observation, I myself have always used "model" in both cases. $\endgroup$ – Willie Wheeler Jan 24 '14 at 17:30

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