Relation of loudness to loudness just noticeable difference of tone

A relation of loudness to loudness just noticeable difference (JND) is derived based on signal detection theory and the hypothesis that loudness is the nerve spike count in the duration of T, and the spike rate distribution of stable tonal stimulus is a stable normal stochastic process. The relation suggests that ratio of louduess JND to loudness of tone is independent of intensity, which can explain well experimental results about the relation of intensity JND to intensity of tone, especially those that could not be explained before such as the Weber fraction hump at the moderate level and the near miss to Weberʹs law.