Probability Distribution of Some Psychophysical Latency Intervals: A Theoretical Study

Abstract

In repeated independent trials, an ideal device integrates the energy of a sinusoidal signal embedded in band-limited Gaussian white noise. Whenever the energy accumulated in the integrator reaches a fixed threshold value, a pulse is triggered. The latency of this pulse, with respect to the on-set of the input, will be a random variable whose distribution is an inverse function of the noncentral chi-squared distribution. Three parameters affect the latency: signal-to-noise ratio, threshold level, and noise bandwidth. For different threshold levels, families of probability density functions are skewed; both their means and variances increase with decreasing signal-to-noise ratio and with increasing threshold; the noise bandwidth acts as a scalar of the coordinate system.