# Is population size a parameter, or sample size a statistic?

The definitions of a parameter and statistic pretty much agree: parameters and statistics are numerical characteristics or numerical summaries of a population and sample, respectively, for a given study. I don't think this is common usage, but...

Could the population size $$N$$ be considered a parameter? Could the sample size $$n$$ be considered a statistic?

After all, the size of the population or sample is a numerical summary or characteristic of the population or sample.

A “parameter” is a knob you turn to get some distribution to behave a certain way. If you want a normal distribution centered at 7, turn $$\mu$$ up to 7. If you want it spread out a lot, turn $$\sigma^2$$ up to 81.
I say that a parameter is some characteristic of a distribution (in the mathematical sense of being a CDF). Therefore, population size is $$\infty$$ and not a parameter.
I agree with the answer given by @Dave (+1) in most aspects. I also agree with the "philosophical" sentiment that population size should usually be considered $$\infty$$ and therefore not a parameter.