Statistics of the interaural parameters for dichotic tones in diotic noise ($N_0 S_ψ$)

Stimuli consisting of an interaurally phase-shifted tone in diotic noise -- often referred to as $N_0 S_\psi$ -- are commonly used in the field of binaural hearing. As a consequence of mixing diotic noise with a dichotic tone, this type of stimulus contains random fluctuations in both interaural phase- and level-difference. This study reports the joint probability density functions of the two interaural differences as a function of amplitude and interaural phase of the tone. Furthermore, a second joint probability density function for interaural phase differences and the instantaneous power of the stimulus is derived.