This paper presents a statistical description of polarization dependent chr
omatic dispersion (PCD) in optical fibers due to second-order polarization
mode dispersion (PMD). This chromatic dispersion is the cause of pulse broa
dening and compression of the signal components propagating in the principa
l states of polarization, We show here that, remarkably, the probability de
nsity function of PCD has the form of the energy density of a first-order o
ptical soliton. We report measurements that are in agreement with the predi
ction of this soliton density. Moreover, since a large number of independen
t experimental samples are difficult to obtain, me also report simulations
of the experimental process and these serve to underscore the agreement bet
ween theory and measurement. The probability density functions of first and
second-order PMD vectors are spherically symmetric, However, these vectors
are not statistically independent, The mean square depolarization with res
pect to wavelength of a launched pulse is revealed to be 33% stronger than
expected for spherical symmetry in the absence of dependence, while the mea
n square PCD is weaker by 67%.