Statistics for The theoretical model for realization of an all-fiber, polarization independent Group Velocity Dispersion (GVD) compensating module with transfer function given by Chebyshev polynomials of the second kind is proposed and investigated. The proposed realization of the GVD compensating module comprises of Mach-Zender interferometers formed by single mode fiber optic directional couplers. The realization of GVD compensating modules using single mode fiber optic couplers as proposed in this paper is superior to an earlier realization of a similar GVD compensating module, which used bulk optic components such as TiO<inf>2</inf> birefringent crystals, polarizers and ?/4 plates. © by Fachverlag Schiele & Schön 2005.