A Maximum Entropy Alternative to the U-shaped Distribution for the Evaluation of Mismatch Uncertainty in Radio-frequency and Microwave Measurements

The Maximum Entropy probability density function associated with the testable information on the range and the first and second order moments of the random quantity of interest is derived. The validity of such approach is experimentally demonstrated through comparison between the proposed maximum entropy distribution and the Ushaped distribution. The underlying physical assumptions which must be satisfied for the proper use of the U-shaped distribution are revisited in the context of wide-band applications, such as Electromagnetic Compatibility measurements.