Another issue is the analog side. I doubt that you'll achieve the 0.1% or so accuracy necessary for this test with the standard Arduino ADC, so you need to design a precision current source and external ADC.
You don't need the Arduino to have great accuracy.
If you were measuring a whole batch of say 1k resistors, you would just make a bridge with another calibrated 1K 0.01% adjusted resistor, a DC source (a battery is fine) and a precise 2:1 divider. The Arduino only has to measure the difference, so if you set it up to be able to measure +/- 5% with a suitable amplifier in front of it, then it can accurately resolve down to 0.01% errors.
The range can be adjusted to be as tight as you want, so you could set the range to +/- 0.1% and resolve errors down to +/- 0.0002% - as long as the reference resistor and the 2:1 divider were accurate enough.
Once the rig is set up, all you need is to change the reference resistor for whatever value you want to test. Even if the reference resistor is of unknown accuracy, if it is stable then the Arduino can accurately measure the variation of resistor values. So you could get an accurate distribution curve - you just wouldn't be sure exactly what the center of the curve is.
Calibrating 2:1 dividers to any accuracy you want is easy - doesn't need any precision equipment.
The one particular thing you have to watch out for in a bridge like this is the reference resistor will gradually warm up, and if it is just s standard cheap resistor, it will drift. So you would want to test a resistor, test a whole bunch of other resistors, then return to measure the first again, and see how much the drift is.
The rig would work just as well for capacitors and inductors.
Richard.