Wireless sensor networks (WSNs) have seen a tremendous growth in various application areas despite prominent performance and availability challenges. Although researchers continue to address these challenges, the type of distributions for arrivals at the cluster head and intermediary routing nodes is still an interesting area of investigation. The general practice in published works is to compare an empirical exponential arrival distribution of WSNs with a theoretical exponential distribution in a Q-Q plot diagram. In this paper, we show that such comparisons based on simple eye checks are not sufficient since, in many cases, incorrect conclusions may be drawn from such plots. After estimating the maximum likelihood parameters of empirical distributions, we generate theoretical distributions based on the estimated parameters. By conducting Kolmogorov-Smirnov test statistics for each generated inter-arrival time distributions, we find out, if it is possible to represent the traffic into the cluster head by using theoretical distribution. Empirical exponential arrival distribution assumption of WSNs holds only for a few cases. The work is further extended to understand the effect of delay on inter-arrival time distributions based on the type of medium access control (MAC) used in WSNs.