Q:

Types of Exoplanets

We discover vastly more exoplanets that are gas giants that orbit their parent star very closely, than small terrestrial planets that are more distant to their sun. Could this be due to the methods we use to find exoplanets?
Gas giants have stronger gravity which makes their star oscillate more. Moreover they are larger which eclipses more of the light of the star during transits?  Are big hot Jupiters far easier to detect than small rocky worlds?

A:

Any statement about the relative frequencies of exoplanets of different size, is limited to the parameter space over which they can detected.
A recent analysis of the Kepler-discovered exoplanets, that takes account of observational selection biases, indicates that for planets orbiting with periods less than about 85 days, that "small Neptune"-sized objects (a few Earth-radii in size) are slightly more common (20%) than Earth-sized objects (17%), which are in turn much more common than Jupiter-sized objects (few %).
Extending this comparison outside this range of orbital periods is not possible with present data (though the paper was in 2013 and things may have now moved on a little).
I never did attach a reference: Here it is https://www.cfa.harvard.edu/news/2013-01

