Compound Poisson Law Research Articles

Protein fluorescence decay: discrete components or distribution of lifetimes? Really no way out of the dilemma?

A new methodology of fluorescence decay analysis by iterative reconvolution is presented. It is based on the recent finding that the statistics of single-photon time-correlated data are best described by a compound Poisson law and requires the recording of a sample of at least 20 decays. Application of multivariate statistical methods to the analysis of the recovered decay parameters results in improved accuracy and better estimation of the uncertainties of mono- and multiexponential decays. If it is, of course, not possible to distinguish unambiguously between discrete components and a continuous distribution of lifetimes, it is, however, possible to determine a higher limit of the width of such a distribution should it be present. With our methodology, the presence of a distribution of lifetimes with a width of approximately 20% of its center value inevitably leads to a failure in the deconvolution procedure, a fact of crucial importance in protein conformational studies, for example.

Some Limit Theorems on Distributional Patterns of Balls in Urns

In an independent, equiprobable allocation urn model, there are various Poisson and normal limit laws for the occupancy of single urns. Applying the Chen-Stein method, we obtain Poisson, compound Poisson and multivariate Poisson limit laws, together with estimates of their rates of convergence, for the number of chunks of $\kappa$ (fixed) adjacent urns occupied by certain numbers of balls distributed in some specified patterns. Several related results on occupancy, waiting time and spacings at certain random times are also presented.

Limit Theorems for Measures on Nonmetrizable Locally Compact Abelian Groups

In a recent book, Parthasarathy provides limit theorems for sums of independent random variables defined on a metrizable locally compact abelian group. These results make heavy use of the metric assumption. This paper consists of a reworking of certain results contained in Parthasarathy to see what can be done without the metric restriction. Among the topics considered are: necessary and sufficient conditions for a limit law to have an idempotent factor; the relationship between limits of compound Poisson laws and limits of sums of independent random variables; and a representation theorem for certain limit laws.

Limit theorems for measures on nonmetrizable locally compact abelian groups

In a recent book, Parthasarathy provides limit theorems for sums of independent random variables defined on a metrizable locally compact abelian group. These results make heavy use of the metric assumption. This paper consists of a reworking of certain results contained in Parthasarathy to see what can be done without the metric restriction. Among the topics considered are: necessary and sufficient conditions for a limit law to have an idempotent factor; the relationship between limits of compound Poisson laws and limits of sums of independent random variables; and a representation theorem for certain limit laws.

The statistical distribution of particle number in an avalanche chain

An expression has been derived for the probability distribution of the total number of electrons and ions in the avalanche chain which develops in a low pressure gas in a high electric field when single avalanches generate successors by photo-electric effect at the cathode. The analysis is based on the assumption that individual avalanche distributions are governed by a simple type of compound Poisson law. The resultant formula has been shown to give correct results when applied to the two special cases for which independent calculations are available.

Statistics and Timing of the First Photoelectron with a High Gain Dynode Photomultiplier

Various types of time interval distributions are calculated assuming a compound Poisson law for the photoelectron emission. The experimental results obtained with the high gain first dynode photomultiplier RCA C 31000 D are discussed with reference to an exponential illumination function. Time resolution curves are measured by performing first photoelectron triggering.

Noise Spectrum of a Stationary Current with Fluctuating Mean

An analysis of the noise generated in an emission current which is governed by a compound Poisson law gives the result that the usual shot-noise term is supplemented by a singular low-frequency flicker-noise component. It is shown that the close mathematical relationship between the two noise sources, disclosed by the analysis, may be of value for the description of flicker noise as observed in real systems.