Measurement of Quality of Service (QoS) parameters and its statistical analysis becomes a key issue for Mobile WiMAX service providers to manage the converged network efficiently and to support end-to-end QoS. In this paper, we investigate the population distribution of end-to-end one-way delay which is the most important QoS parameter in Mobile WiMAX networks. The samples are analyzed with Chi-Square Goodness-of-Fit test, Kolmogorov-Smirnov (K-S), and Anderson-Darling (A-D) test to verify the distribution of parent population. The relation with confidence level and the minimum number of sample size is also performed for logistic distribution. The statistical analysis is a promising approach for measuring the performance Mobile WiMAX networks.