The majority of activity recognition systems in wearable computing rely on a set of statistical measures, such as means and moments, extracted from short frames of continuous sensor measurements to perform recognition. These features implicitly quantify the distribution of data observed in each frame. However, feature selection remains challenging and labour intensive, rendering a more generic method to quantify distributions in accelerometer data much desired. In this paper we present the ECDF representation, a novel approach to preserve characteristics of arbitrary distributions for feature extraction, which is particularly suitable for embedded applications. In extensive experiments on six publicly available datasets we demonstrate that it outperforms common approaches to feature extraction across a wide variety of tasks.