Non-Gaussian data is encountered in a variety of fields. To make reliable judgement and reasonable simulation, it is important to establish an appropriate probability density function(PDF) model for non-Gaussian data. In this book, three PDF models are studied to represent the distribution of non-Gaussian data. They are Pade-Laplace Method, Maximum Entropy Method and Hermite Polynomial Method. Also, test of goodness of fit are conducted among the proposed PDF models and common PDF models to compare the flexibility and robustness of these PDF models.