In general, one of the most important aspects of software development and project management is how to make predictions and assessments of quality and reliability for developed products. Project data usually will be systematically collected and analyzed during the process of software development. Practically, it would be helpful if developers could identify the most error-prone modules early so that they can optimize testing-resource allocation and increase fault detection effectiveness accordingly. In the past, many research studies revealed the applicability of the Pareto principle to software systems, and some of them reported that the Pareto distribution (PD) model can be used to predict the fault distribution of software. In this paper, a special form of the Generalized PD model, named the Bounded Generalized Pareto distribution (BGPD) model, is further proposed to investigate the fault distributions of Open Source Software (OSS). It can be seen that the BGPD model eliminates the issue which occurred in the classical PD model. Three methods of parameter estimation will be presented, and related experiments are performed based on real OSS failure data. Experimental results show that the BGPD model presents high fitness to the actual failure data of OSS. Finally, the possibility of using early limited fault data to predict the later software fault distribution is also studied. Numerical results indicate that the BGPD model can be trusted to consistently produce accurate estimates of fault predictions during the early stages of development. The findings can provide an effective foundation for managing the necessary activities of software development and testing.