Stable distributions are important family of parametric distributions widely used in signal processing as well as in mathematical finance. Estimation of the parameters of this model, is not quite straightforward due to the fact that there is no closed-form expression for their probability density function. Besides the computationally intensive maximum likelihood method where the density has to be evaluated numerically, there are some existing adhoc methods such as the quantile method, and a regression based method. These are introduced in Chapter 2. In this thesis, we introduce two new approaches: One, a spacing based estimation method introduced in Chapter 3 and two, an indirect inference method considered in Chapter 4. Simulation studies show that both these methods are very robust and efficient and do as well or better than the existing methods in most cases. Finally in Chapter 5, we use indirect inference approach to estimate the best fitting income distribution based on limited information that is often available.