The generalized lambda distribution (GLD) is very useful in fitting data and approximating many well know distributions. Since the GLD is defined by its quantile function, it can provide a simple and effective algorithm for generating random variates. The purpose of this dissertation is to estimate the four parameters of the GLD by using two methods, the method of moments and the method of least squares. A Monte Carlo experiment was conducted to perform a comparison between the two methods in estimating the four parameters of the GLD and fitting the data. The results of this experiment show that the method of least squares appears to produce slightly better fits than the method of moments especially in the cases of the right skewed distributions. Also, the absolute difference between the theoretical lambda and the estimated lambda is smaller in the case of the least squares than the method of moments. Also, numerical examples were used to estimate the parameters of the GLD and a comparison of the least squares with the method of moments were provided. The method of moments only converged in two out of 20 data sets, whereas, the method of least squares converged in all 20 data sets. A computer program written in Fortran is also provided.