Taking in account that the solar energy received on planet decreases as $1/r^2$, there you have a direct relation. Far planets are much colder and able to condensate gases that otherwise will be lost, closer ones are rocks with very little atmosphere. But going further from Jupiter(which is almost hydrogen) this doesnot matter anymore and they will more or less have a constant composition.
But a lot of other factors have to be taken in account(original structure of the cloud in which planets where formed, atmosphere, solar pressure, etc) so I believe that statistic about this are quite inconclusive with so little data to consider.
