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PubMed1985

An intervened Poisson distribution and its medical application.

Among probability distributions that are used to describe a chance mechanism whose observational apparatus becomes active only when at least one event occurs is the zero-truncated Poisson distribution (ZTPD). A modified version of the ZTPD, which we call an intervened Poisson distribution (IPD), is discussed in this paper. We give a genesis of IPD and obtain its statistical properties. A numerical example is included to illustrate the results.

Biometry↗
PubMed1993

Luria-Delbrück fluctuation analysis: estimating the Poisson parameter in a compound Poisson distribution.

Estimating the mutation rate from a Luria-Delbrück fluctuation experiment involves estimating the Poisson parameter in a compound Poisson distribution. The efficiency with which this can be estimated depends on how well the other random factors have been characterized. The assumption that cell growth can be represented as a stochastic pure birth or Yule process is biologically unrealistic but contributes little to the bias and variance of a maximum likelihood estimator of the mutation rate.

Algorithms↗
PubMed2003

A microdosimetric-kinetic model for the effect of non-Poisson distribution of lethal lesions on the variation of RBE with LET.

The microdosimetric-kinetic (MK) model for cell killing by ionizing radiation is summarized. An equation based on the MK model is presented which gives the dependence of the relative biological effectiveness in the limit of zero dose (RBE1) on the linear energy transfer (LET). The relationship coincides with the linear relationship of RBE1 and LET observed for low LET, which is characteristic of a Poisson distribution of lethal lesions among the irradiated cells. It incorporates the effect of deviation from the Poisson distribution at higher LET. This causes RBE1 to be less than indicated by extrapolation of the linear relationship to higher LET, and to pass through a maximum in the range of LET of 50 to 200 keV per micrometer. The relationship is compared with several experimental studies from the literature. It is shown to approximately fit their results with a reasonable choice for the value of a cross-sectional area related to the morphology and ultrastructure of the cell nucleus. The model and the experiments examined indicate that the more sensitive cells are to radiation at low LET, the lower will be the maximum in RBE they attain as LET increases. An equation that portrays the ratio of the sensitivity of a pair of cell types as a function of LET is presented. Implications for radiotherapy with high-LET radiation are discussed.

Cell Line↗
PubMed2000

Calculation of interspike intervals for integrate-and-fire neurons with poisson distribution of synaptic inputs.

We present a new technique for calculating the interspike intervals of integrate-and-fire neurons. There are two new components to this technique. First, the probability density of the summed potential is calculated by integrating over the distribution of arrival times of the afferent post-synaptic potentials (PSPs), rather than using conventional stochastic differential equation techniques. A general formulation of this technique is given in terms of the probability distribution of the inputs and the time course of the postsynaptic response. The expressions are evaluated in the gaussian approximation, which gives results that become more accurate for large numbers of small-amplitude PSPs. Second, the probability density of output spikes, which are generated when the potential reaches threshold, is given in terms of an integral involving a conditional probability density. This expression is a generalization of the renewal equation, but it holds for both leaky neurons and situations in which there is no time-translational invariance. The conditional probability density of the potential is calculated using the same technique of integrating over the distribution of arrival times of the afferent PSPs. For inputs with a Poisson distribution, the known analytic solutions for both the perfect integrator model and the Stein model (which incorporates membrane potential leakage) in the diffusion limit are obtained. The interspike interval distribution may also be calculated numerically for models that incorporate both membrane potential leakage and a finite rise time of the postsynaptic response. Plots of the relationship between input and output firing rates, as well as the coefficient of variation, are given, and inputs with varying rates and amplitudes, including inhibitory inputs, are analyzed. The results indicate that neurons functioning near their critical threshold, where the inputs are just sufficient to cause firing, display a large variability in their spike timings.

Action Potentials↗
PubMed1999

Sister chromatid exchange data fit with a mixture of Poisson distributions.

Bowman et al. [K.O. Bowman, Wesley Eddings, Marvin A. Kastenbaum, L. R. Shenton. Sister chromatid exchange data and Gram-Charlier series, Mutat. Res., 403 (1998) 159-169.] have shown that a Gram-Charlier modification of a negative binomial distribution gives a reasonable fit to counts of sister chromatid exchange (SCE) data originally presented by Bender et al. [M.A. Bender, R.J. Preston, R. C. Leonard, B.E. Pyatt, P.C. Gooch, On the distribution of spontaneous SCE in human peripheral blood lymphocytes, Mutat. Res., 281 (1992) 227-232. ]. Here we show that a mixture of a generalized Poisson distributions also fits the data. Advantages of the generalized Poisson mixture include a simplified model involving only four parameters which fits the data more closely according to the chi-squared goodness-of-fit criterion.

Female↗
PubMed1990

A Monte Carlo study of tests on data originating from quadrat sampling. I: Data from a Poisson distribution.

Computer simulations are used to examine the significance levels and powers of several tests which have been employed to compare the means of Poisson distributions. In particular, attention is focused on the behaviour of the tests when the means are small, as is often the case in ecological studies when populations of organisms are sampled using quadrats. Two approaches to testing are considered. The first assumes a log linear model for the Poisson data and leads to tests based on the deviance. The second employs standard analysis of variance tests following data transformations, including the often used logarithmic and square root transformations. For very small means it is found that a deviance-based test has the most favourable characteristics, generally outperforming analysis of variance tests on transformed data; none of the latter appears consistently better than any other. For larger means the standard analysis of variance on untransformed data performs well.

Analysis of Variance↗
PubMed1997

[Increasing use of heroine and cocaine in Switzerland since 1990: use of a generalized Poisson distribution in the collected data].

Estimates of the prevalence of deviant behaviour, which are based on the usual survey methods are by far too low. Therefore, the use of capture-recapture methods or of the truncated Poisson distribution is to be preferred, provided appropriate data are available. Here an extended Poisson approach was applied in order to estimate the number of users of hard illegal drugs (heroin, cocaine) in Switzerland for each year from 1990 to 1993. These estimates indicate an increase by about 50% during the period 1990-1993.

Adolescent↗
PubMed2004

A measurement error model with a Poisson distributed surrogate.

We study a linear model in which one of the covariates is measured with error. The surrogate for this covariate is the event count in unit time. We model the event count by a Poisson distribution, the rate of which is the unobserved true covariate. We show that ignoring the measurement error leads to inconsistent estimators of the regression coefficients and propose a set of unbiased estimating equations to correct the bias. The method is computationally simple and does not require using supplemental data as is often the case in other measurement error analyses. No distributional assumption is made for the unobserved covariate. The proposed method is illustrated with an example from the Wisconsin Sleep Cohort Study.

Bias↗
PubMed1994

Precision of incidence predictions based on Poisson distributed observations.

Disease incidence predictions are useful for a number of administrative and scientific purposes. The simplest ones are made using trend extrapolation, on either an arithmetic or a logarithmic scale. This paper shows how approximate confidence prediction intervals can be calculated for such predictions, both for the total number of cases and for the age-adjusted incidence rates, by assuming Poisson distribution of the age and period specific numbers of incident cases. Generalizations for prediction models, for example, using power families and extra-Poisson variation, are also presented. Cancer incidence predictions for the Stockholm-Gotland Oncological Region in Sweden are used as an example.

Adult↗
PubMed2007

A random-effects Markov transition model for Poisson-distributed repeated measures with non-ignorable missing values.

In biomedical research with longitudinal designs, missing values due to intermittent non-response or premature withdrawal are usually 'non-ignorable' in the sense that unobserved values are related to the patterns of missingness. By drawing the framework of a shared-parameter mechanism, the process yielding the repeated count measures and the process yielding missing values can be modelled separately, conditionally on a group of shared parameters. For chronic diseases, Markov transition models can be used to study the transitional features of the pathologic processes. In this paper, Markov Chain Monte Carlo algorithms are developed to fit a random-effects Markov transition model for incomplete count repeated measures, within which random effects are shared by the counting process and the missing-data mechanism. Assuming a Poisson distribution for the count measures, the transition probabilities are estimated using a Poisson regression model. The missingness mechanism is modelled with a multinomial-logit regression to calculate the transition probabilities of the missingness indicators. The method is demonstrated using both simulated data sets and a practical data set from a smoking cessation clinical trial.

Algorithms↗
PubMed1999

Poisson distribution of male mating success in laboratory populations of Drosophila melanogaster.

Variation among males and females in reproductive success is a major determinant of effective population size. Most studies of male mating success in Drosophila, however, have been done under conditions very different from those in typical cultures. We determined the distribution of male mating success in five laboratory populations of D. melanogaster maintained on a 14 d, discrete generation cycle fairly representative of standard Drosophila cultures. Mating success was measured as the number of matings a male could achieve under conditions closely approximating a regular culture vial of these populations. Preliminary studies determined that most mating in these populations occurred within 14 h of the flies attaining sexual maturity. Consequently, individual virgin males were marked with white paint on their thorax, put into vials with varying numbers of unmarked virgin flies of both sexes, and monitored continuously for matings over a period of up to 14 h. At various times during the assay, virgin males and females were added to these vials in proportions simulating the pattern of eclosion in culture vials. The observed variation in the number of matings per male in the five populations was, by and large, consistent with a Poisson distribution, suggesting that male mating success in short-generation-time, discrete-generation laboratory cultures of D. melanogaster may fulfil a fundamental assumption of the Wright-Fisher model of genetic drift in finite populations.

Animals↗
PubMed2004

Stringent numerical test of the Poisson distribution for finite quantum integrable Hamiltonians.

Using a class of exactly solvable models based on the pairing interaction, we show that it is possible to construct integrable Hamiltonians with a Wigner distribution of nearest-neighbor level spacings. However, these Hamiltonians involve many-body interactions and the addition of a small integrable perturbation very quickly leads the system to a Poisson distribution. Besides this exceptional case, we show that the accumulated distribution of an ensemble of random integrable two-body pairing Hamiltonians is in perfect agreement with the Poisson limit. These numerical results for quantum integrable Hamiltonians provide a further empirical confirmation of the work of Berry and Tabor in the semiclassical limit.

Journal Article↗
PubMed1987

Confirmation of an abnormal (non-Poisson) distribution of sperm from some infertile men in the hamster-ovum test.

The present study was carried out to investigate an earlier report that stated that some men of infertile couples (patients), but not normal donors, have an abnormal (non-Poison) distribution of penetrating sperm among ova in the hamster-ovum test. Semen samples from 60 men, 24 proven fathers and 36 patients, were analyzed for agreement with the theoretical Poisson distribution (PD). Most of the fathers (23 of 24) fit PD well, but 10 of the patients did not. The overall (group) fit of fathers is good, but that of the patients is poor. Patients, but not fathers, are heterogeneous in their agreement with PD; about 25% fit poorly whereas more than 50% fit well. The 25% fitting poorly may often be those patients who are truly infertile (even when their wives are actually fertile).

Adult↗
PubMed2005

Smooth tests for the zero-inflated poisson distribution.

In this article we construct three smooth goodness-of-fit tests for testing for the zero-inflated Poisson (ZIP) distribution against general smooth alternatives in the sense of Neyman. We apply our tests to a data set previously claimed to be ZIP distributed, and show that the ZIP is not a good model to describe the data. At rejection of the null hypothesis of ZIP, the individual components of the test statistic, which are directly related to interpretable parameters in a smooth model, may be used to gain insight into an alternative distribution.

Animals↗
PubMed1975

Non-Poisson distribution in time of small- and large-mode miniature end-plate potentials.

Minature end-plate potentials (MEPP's) were recorded from frog (Rana pipiens) sartorius muscle cells of 60--80 mum diam; MEPP frequency remained constant up to 3 h and was 100 times greater in 80-mum cells than in 6-mum cells. Rapid cooling or heating of preparations initiated or accentuated bursts of MEPP's. Records from cells under control conditions and from cells where the MEPP population had been reduced to the small mode showed many instances of small clusters of MEPP's occurring within 100-ms intervals, indicating quantal release interdependencies. Some small cells initially generated many large MEPP's 2 or more times the average amplitude and fewer small clusters. Analysis of the occurrence of both large- and small-mode MEPP's for both 1.0-s and 100-ms nonoverlapping bins demonstrated a highly significant deviation from a Poisson distribution with significance increasing with decreasing cell diameter and/or MEPP frequency. It is suggested that doublet MEPP's are generated from one release site and that large bursts results from the activity of several release sites, since the size of bursts decreases with cell diameter (junctional area). It is concluded that release characteristics are the same for large-mode (classical) and small-mode MEPP's and that the occurrence of MEPP's is not Poisson.

Animals↗