A probability model for distributions of speech intelligibility data
Caldwell P. Smith · The Journal of the Acoustical Society of America · 1991
It was determined that the compound Poisson probability distribution as described by William Feller in An Introduction to Probability Theory and Its Applications, 2nd ed. [(Wiley, New York, 1975), pp. 270–273] is a valid model for distributions of speech intelligibility scores from diagnostic rhyme tests. This was established from details of scores from 110 multispeaker tests of a variety of speech processing conditions. Probability models were constructed by first converting feature scores to integers representing frequencies of errors in listener responses, and calculating means and variances of those distributions. Variance of a compound Poisson distribution is equal to the mean divided by p, and in this corpus of data the value of p tended to remain relatively fixed at an average value of 0.129, with the consequence that distributions were essentially defined by mean values and dispersions a linear function of means. In these measures, variance averaged 7.75 times the mean, with the average value of this coefficient varying over a limited range with different speech processing conditions: for LPC processors, the average was 8.37; for wideband processors, 7.12; for processors in tandem, 6.75; and for speech in Gaussian noise, 8.06. Partitioned into separate data sets for voiced and unvoiced feature scores, the same trends were observed, but with coefficients approximately 15% larger with voiced data, and approximately 20% smaller with unvoiced data.