Emotion analysis based on peripheral physiological signals has attracted increasing attention recently in affective computing. Previous works usually predict emotional states using a single emotion label for each discrete time. However, in real-world scenarios, it is not sufficient due to the fact that the real-world emotional state is usually a mixture of basic emotions. In this paper, we formulate the emotion analysis as an emotion distribution learning (EDL) problem and make two contributions. First, we establish a standardised dataset containing four negative emotions (anger, disgust, sadness, fear) and three positive emotions (tenderness, joy, amusement), which could be a useful benchmark for the EDL task. Second, we propose an emotion distribution prediction system which has the following distinct characteristics: (1) after processing raw peripheral physiological signals, we compute totally 89 representative features from four channels, i.e., GSR, SKT, ECG and HR, (2) an adaptive feature selection strategy based on recursive feature elimination (RFE) is used to select the most significant features in our EDL task, and (3) we design a dedicated EDL model based on convolution neural networks that takes information from both the feature correlation and the time domain into consideration. Experiments were conducted to validate our proposed system.