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Role of the doubly stochastic Neyman type-A and Thomas counting distributions in photon detection
- APPL. OPT
, 1981
"... The Neyman type-A and Thomas counting distributions provide a useful description for a broad variety of phenomena from the distribution of larvas on small plots of land to the distribution of galaxies in space. They turn out to provide a good description for the counting of photons generated by mult ..."
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The Neyman type-A and Thomas counting distributions provide a useful description for a broad variety of phenomena from the distribution of larvas on small plots of land to the distribution of galaxies in space. They turn out to provide a good description for the counting of photons generated by multiplied Poisson processes, as long as the time course of the multiplication is short compared with the counting time. Analytic
Statistical properties of a nonstationary Neyman–Scott cluster process
- IEEE TRANSACTIONS ON INFORMATION THEORY
, 1983
"... A recurrence relation is obtained for the counting distribution, as well as the probability density of waiting time, for a doubly stochastic Poisson point process driven by nonstationary shot noise (SNDP). For a stimulus of short duration, the counting distribution approximately reduces to the Neyma ..."
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Cited by 4 (4 self)
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A recurrence relation is obtained for the counting distribution, as well as the probability density of waiting time, for a doubly stochastic Poisson point process driven by nonstationary shot noise (SNDP). For a stimulus of short duration, the counting distribution approximately reduces to the Neyman Type-A. The SNDP is an important special Neyman-Scott cluster process.
Thomas point process in pulse, particle and photon detection
- Applied Optics
, 1983
"... Multiplication effects in point processes are important in a number of areas of electrical engineering and physics. We examine the properties and applications of a point process that arises when each event of a primary Poisson process generates a random number of subsidiary events with a given time ..."
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Cited by 4 (3 self)
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Multiplication effects in point processes are important in a number of areas of electrical engineering and physics. We examine the properties and applications of a point process that arises when each event of a primary Poisson process generates a random number of subsidiary events with a given time course. The multiplication factor is assumed to obey the Poisson probability law, and the dynamics of the time delay are associated with a linear filter of arbitrary impulse response function; special attention is devoted to the rectangular and exponential case. Primary events are included in the final point process, which is expected to have applications in pulse, particle, and photon detection. We refer to this as the Thomas point process since the counting distribution reduces to the Thomas distribution in the limit of long counting times. Explicit results are obtained for the singlefold and multifold counting statistics (distribution of the number of events registered in a fixed counting time), the time statistics (forward recurrence time and interevent probability densities), and the counting correlation function (noise properties). These statistics can provide substantial insight into the underlying physical mechanisms generating the process. An example of the applicability of the model is provided by betaluminescence photons produced in a glass photomultiplier tube, when Cherenkov events are also present. I.
unknown title
, 1980
"... Interevent-time statistics for shot-noise-driven self-exciting point processes in photon detection ..."
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Interevent-time statistics for shot-noise-driven self-exciting point processes in photon detection
