One motivation for the model we develop in this chapter is provided by the atmospheric-noise data shown in Fig. 1.3. It is evident that a point process model can account for the occurrence times of the pulses. However, these times alone do not reflect all of the significant features. The amplitudes of the pulses exhibit wide variation and have a strong influence on a radio receiver operating at low frequencies. Even a first-approximation model for low-frequency atmospheric noise should, therefore, include the amplitude as well as occurrence time of each pulse. It is this procedure of endowing each temporal point with an ancillary variable, an amplitude in this instance, which characterizes the models of this chapter.
KeywordsPoisson Process Occurrence Time Counting Process Independent Increment Disjoint Region
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