The distribution of bugs in software systems has been shown to satisfy the Pareto principle, and typically shows a power-law tail when analyzed as a rank-frequency plot. In a recent paper, Zhang showed that the Weibull cumulative distribution is a very good fit for the Alberg diagram of bugs built with experimental data. In this paper, we further discuss the subject from a statistical perspective, using as case studies five versions of Eclipse, to show how log-normal, Double-Pareto, and Yule-Simon distributions may fit the bug distribution at least as well as the Weibull distribution. In particular, we show how some of these alternative distributions provide both a superior fit to empirical data and a theoretical motivation to be used for modeling the bug generation process. While our results have been obtained on Eclipse, we believe that these models, in particular the Yule-Simon one, can generalize to other software systems.