Parametric Distributions to Model Numerical Emotion Labels

It is common to represent emotional states as values on a set of numerical scales corresponding to attributes such as arousal and valence. Often these labels are obtained from multiple annotators who record their perception of emotion in terms of these attributes. Combining these multiple annotations by taking the mean, as is typical in affective computing systems ignores the inherent ambiguity in the labels. Recently it has been recognised that this ambiguity carries useful information and systems that employ distributions over the numerical scales to represent emotional states have been proposed. In this paper we show that the common and widespread assumption that this distribution is Gaussian may not be suitable since the underlying numerical scales are bounded. We then compare a range of well-known distributions defined on bounded domains to ascertain which of them would be the most suitable alternative. Statistical measures are proposed to enable quantifiable comparisons and the results are reported. All comparisons reported in the paper were carried out on the RECOLA dataset.