s. For most installed systems, we can nearly always assume the square root behavior. The Statistical Nature of PMD Understanding the statistical character of PMD is essential for understanding the perfor- mance of a real system. If the DGD of a long fiber link is measured many times, it can be expected to exhibit a range of values. Therefore, we must deal with probability distributions. The probability density function for DGDs in a long-span optical fiber is known as a "Max- wellian distribution," and its validity has been confirmed by many experimental studies (Poole & Nagel, 1997; Bülow & Lanne, 2005). The function is plotted in Figure 6.28, which shows that it is asymmetric with a value of zero when At = 0. The mean value of the Max- wellian is <AT> and, because of the asymmetry, it is slightly higher than the value corre- sponding to the peak. It is to the mean that we refer when specifying a fiber's PMD (in ps/km2. The long "tail" of the Maxwellian distribution to higher values of At is important because it opens the possibility of rare events, in which the DGD can be unusually large and SO cause substantial pulse separation (Neslon & Jopson, 2005). The lower graph in Figure 6.28 shows the Maxwellian probability distribution function integrated from At to infinity. The statistical nature of PMD means that it exerts different influences compared with other more deterministic phenomena, such as chromatic dispersion and nonlinear crosstalk. A key feature is that DGD varies over time. Some effects, such as day-to-night temperature variations, are slow; others, however, such as vibrations caused by human activities, occur on a much shorter timescale. Some environments are relatively stable, such as cables on the sea bed. Others, such as "aerial fibers," where the cables are suspended overhead from poles, are subject to weather variations. In a given environment, the consequence of random fluctuations is that the DGD can explore a wide range of values. The top graph of Figure 6.28 shows that low-probability event