Why LED reversed bias voltage cannot be measured?
LEDs behave electrically like other types of diodes, just with different parameters. They can be modeled reasonably well by the Shockley diode equation with a series resistor. 



Regular diodes tend to have a reverse breakdown in the 50V-1000V range, LEDs it's on the lower end of that range. Usually we don't use LEDs reverse biased except to stand off a few volts in multiplexed circuits, so the specs tend to be very loose (maybe a 5V spec on an LED that can withstand 50V or 100V of reverse bias). 

Regular diodes have a forward voltage of 0.6V or so at currents of mA, with LEDs it's more like 1V-3.5V (the lower values for IR LEDs, the higher for UV). 

The ideality factor n tends to be around 2 for regular diodes, and it can be quite different for LEDs.