Automated program repair has been used to provide feedback for incorrect student programming assignments, since program repair captures the code modification needed to make a given buggy program pass a given test-suite. Existing student feedback generation techniques are limited because they either require manual effort in the form of providing an error model, or require a large number of correct student submissions to learn from, or suffer from lack of scalability and accuracy. In this work, we propose a fully automated approach for generating student program repairs in real-time. This is achieved by first re-factoring all available correct solutions to semantically equivalent solutions. Given an incorrect program, we match the program with the closest matching refactored program based on its control flow structure. Subsequently, we infer the input-output specifications of the incorrect program's basic blocks from the executions of the correct program's aligned basic blocks. Finally, these specifications are used to modify the blocks of the incorrect program via search-based synthesis. Our dataset consists of almost 1,800 real-life incorrect Python program submissions from 361 students for an introductory programming course at a large public university. Our experimental results suggest that our method is more effective and efficient than recently proposed feedback generation approaches. About 30% of the patches produced by our tool Refactory are smaller than those produced by the state-of-art tool Clara, and can be produced given fewer correct solutions (often a single correct solution) and in a shorter time. We opine that our method is applicable not only to programming assignments, and could be seen as a general-purpose program repair method that can achieve good results with just a single correct reference solution.
In this paper, we present a nonparametric estimator for ruin probability in the classical risk model with unknown claim size distribution. We construct the estimator by Fourier inversion and kernel density estimation method. Under some conditions imposed on the kernel, bandwidth and claim size density, we present some large sample properties of the estimator. Some simulation studies are also given to show the finite sample performance of the estimator.
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