A demystification of the U-shaped probability distribution

A measurement uncertainty calculation involves the consideration of several different probability distributions. Of those considered, the U-shaped distribution is generally least familiar to the typical EMC engineer. This paper attempts to demystify the U-shaped distribution by studying a situation in which the distribution occurs naturally (the Voltage Standing Wave (VSW) amplitude generated along a cable by impedance mismatch at its termination). An analytical expression for the probability distribution is derived and shown to be U-shaped.