With the detection of gravitational waves a new window for astronomy has opened. Pulsar timing arrays are looking for gravitational waves emitted by supermassive black hole binaries. They are assumed to be in the center of massive galaxies. As they spiral into each other they will go through different phases of evolution and emit gravitational waves. We assume a simple model where the binary evolution changes from being driven by stellar hardening of the environment to being driven by emission of gravitional waves. At a certain turnover frequency we assume that each binary will have a fixed eccentricity. The emitted spectrum is described by a population function and eccentricity. Using Bayesian methods we analyse these physical parameters by means of MCMC simulations. We check an upperlimit and a detection case to see what information we can derive from pulsar timing array observations.