Poissonmodulated

Poissonmodulated refers to a phenomenon or process where a signal or event occurs randomly according to a Poisson distribution, and this underlying randomness is then modulated or influenced by another factor. In essence, it combines two sources of variability. The Poisson distribution itself describes the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. Examples of pure Poisson processes include the number of radioactive decays in a given time or the number of customers arriving at a service desk in an hour, assuming constant arrival rates.

When Poissonmodulated, the rate parameter of the Poisson distribution is no longer constant but varies over time or space in a predictable or stochastic way. For instance, the arrival rate of customers at a store might follow a Poisson process, but this rate could be modulated by the time of day, with higher rates during peak hours and lower rates during off-peak times. Similarly, the occurrence of certain biological events might be Poisson-distributed, but their frequency could be modulated by environmental factors. Analyzing Poissonmodulated systems often involves more complex statistical models than those used for simple Poisson processes, as it requires accounting for both the inherent randomness of the Poisson events and the superimposed modulation.