Fluid antenna systems (FAS) are an emerging technology that promises a significant diversity gain even in the smallest spaces. It consists of a freely moving antenna in a small linear space to pick up the strongest received signal. Previous works in the literature provide a simple yet insightful parameterization of the FAS channel that leads to single-integral expressions of the probability of outage and various insights on the achievable performance. Nevertheless, this channel model may not accurately capture the correlation between the FAS ports, given by Jake's model. This work builds on the state-of-the-art by incorporating more parameters into the channel model to accurately approximate the FAS channel distribution while maintaining analytical tractability. The approximation is performed in two stages. The first stage approximation considerably reduces the number of multi-fold integrals in the probability of outage expression, while the second stage approximation represents it in a single integral form. Numerical results validate our approximations of the FAS channel model and demonstrate a limited performance gain under a more accurate correlation model. Further, our work opens the door for future research to investigate scenarios in which the FAS provides a performance gain compared to the current multiple antenna solutions.