ABSTRACT
It can be mathematically derived that under certain conditions, the number of event occurrences in a fixed period of time obeys a Poisson distribution. For example, over a fixed period, the distribution of the number of action potentials (which is a discrete random variable) in an auditory nerve fiber in response to a speech stimulus can be approximated by a Poisson distribution (especially when the refractoriness is ignored). If the fixed period is reasonably short over which the speech spectral information does not change substantially, the Poisson rate A may be constant. Otherwise, we will have a variable-rate Poisson distribution over the observation time interval. Another example of a Poisson distribution is the number of data packets (such as digitally coded speech) observed over a fixed period of time in a telecommunication network (e.g., [Deng 93d]).
Binomial and multinomial distributions
