González-Torre, I. 1, 3 , Luque , B. 1 , Lacasa, L. 2 , Kello, C. T. 3 & Hernández-Fernández, A. 4
1 Departamento de Matemática Aplicada ETSIAE; Universidad Politécnica de Madrid; Plaza Cardenal Cisneros 28040 Madrid (Spain)
2 School of Mathematical Sciences; Queen Mary University of London; Mile End Road E14NS London (UK)
3 Cognitive and Information Sciences University of California , Merced, 5200 North Lake Rd., Merced, CA 95343, USA
4 Complexity and Quantitative Linguistics Lab; Laboratory for Relational Algorithmics; Complexity and Learning (LARCA); Institut de Ciències de l?Educació; Universitat Politècnica de Catalunya, Barcelona (Catalonia, Spain)
In this work we verify with accuracy that acoustically transcribed durations of linguistic units at several scales (phonemes, words and Breath Groups) comply with log-normal distribution. To do this we have used a very well-known Corpus which contains conversational speech by native English speakers gathering approximately 300000 words with time-aligned phonetic labels.
Secondly, we explain this log-normal distribution using a new model: a Non-interacting Cascade Approach (NICA) model. This NICA model can explain the emergence of Lognormal distributions across linguistic levels (words, Breathe Group) solely based on the assumption that phoneme durations are also Lognormal. As we will see, we find an extremely good quantitative agreement between the NICA and the experimental results of the duration distribution for the case of phonemes and words, but such agreement is less spectacular in the case of Breath Groups.
Finally, we discuss our results and justify our recommendation to work with medians instead of with mean values (that assumes Gaussian distribution) to avoid biases and erroneous conclusions in statistical learning studies based on acoustic elements with long-tailed distributions.