infinity, NaN in band statistics

[bossie]

So we've run into this case where GDAL reports e.g. a maximum of Infinity and a mean of NaN for a raster.

Should the specification for the Statistics Object not be updated to allow these special values like nodata does?

[m-mohr]

STAC sprint:

For statistics, I think we should clarify that basically -infinity is the default for minimum and +infinity is the default for maximum.
nan for statistics doesn't make a lot of sense to me. Why not just omit the property then?
Having strings in the statistics seems like a bad idea to us.
Let's also add count field.

[m-mohr]

Is now present as part of the Bands RFC.