This study establishes the new results for Cluster Width of probability Density functions (CWD). There are the upper and lower bounds of CWD and the relationships of CWD to other measures in statistical discriminant. The CWD for two and more two probability density functions is determined in the different cases. Based on CWD, we propose a measure called similar coefficient to evaluate the quality of the established clusters. Furthermore, CWD is also used as a criterion to build two algorithms: to determine the suitable number of clusters and to analyse the fuzzy clusters. The numerical examples are given to illustrate the proposed algorithms and to prove their advantages over existing methods.