Characterizing the distribution of the quadrilateral vowel space area

The vowel space area (VSA) has been studied as a quantitative index of intelligibility to the extent it captures articulatory working space and reductions therein. The majority of such studies have been empirical wherein measures of VSA are correlated with perceptual measures of intelligibility. However, the literature contains minimal mathematical analysis of the properties of this metric. This paper further develops the theoretical underpinnings of this metric by presenting a detailed analysis of the statistical properties of the VSA and characterizing its distribution through the moment generating function. The theoretical analysis is confirmed by a series of experiments where empirically estimated and theoretically predicted statistics of this function are compared. The results show that on the Hillenbrand and TIMIT data, the theoretically predicted values of the higher-order statistics of the VSA match very well with the empirical estimates of the same.