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Software defects play a key role in software reliability, and the number of remaining defects is one of most important software reliability indexes. Observing the trend of the number of remaining defects during the testing process can provide very useful information on the software reliability. However, the number of remaining defects is not known and has to be estimated. Therefore, it is important to study the trend of the remaining software defect estimation (RSDE). In this paper, the concept of RSDE curves is proposed. An RSDE curve describes the dynamic behavior of RSDE as software testing proceeds. Generally, RSDE changes over time and displays two typical patterns: 1) single mode and 2) multiple modes. This behavior is due to the different characteristics of the testing process, i.e., testing under a single testing profile or multiple testing profiles with various change points. By studying the trend of the estimated number of remaining software defects, RSDE curves can provide further insights into the software testing process. In particular, in this paper, the Goel-Okumoto model is used to estimate this number on actual software failure data, and some properties of RSDE are derived. In addition, we discuss some theoretical and application issues of the RSDE curves. The concept of the proposed RSDE curves is independent of the selected model. The methods and development discussed in this paper can be applied to any valid estimation model to develop and study its corresponding RSDE curve. Finally, we discuss several possible areas for future research.