Compound Intervened Poisson Distribution

The nature and characteristics of Intervened Poisson Distribution (IPD) has been well discussed by Shanmugam (1985). In this paper, Compound Intervened Poisson Distribution (CIPD) is introduced and its properties are studied.     

Quantification of the dose-Mortality response of Trichoplusia ni,Helioithis, zea,and Spodoptera frugiperda to Nuclear polyhedrosis viruses: Applicability of an exponential model

In vivo assays of several nuclear polyhedrosis viruses were conducted in neonate Trichoplusia ni, Heliothis zea, and Spodoptera frugiperda larvae using a droplet feeding method. Characteristic deviations from the probit model were observed with several virus isolats that suggested the dose-reponse relation might be determined primarily by the chance of obtaining virus from the inoculum rather than by variabilityin host susceptibility. This was supported by comparisons of the slopes of the probit lines with the corresponding expected values based on the exponential relationship described by a one-hit Poissonian curve. Where applicable, the exponential model offers severl advantages over the probit model in describing and quantifying virus-host relations.     

The Multiple Poisson Distribution,Its Characteristics and a Variety of Forms

The multiple Poisson distribution, known under different names, such as generalized Poisson, compound Poisson, composed Poisson, stuttering Poisson, Poisson power series, Poisson-stopped sum distribution, etc., plays an important role in discrete distribution theory. Here we want to show its basic characteristics, the variety of its forms and specify the generalizing distributions.     

Statistically Estimated Free Energies of Chromosome Aberration Production from Frequency Data

Janardan and Schaeffer (1977) suggested that the Lagrangian Poisson Distribution (LPD) could be used to estimate the net free energy for the production of induced chromosome aberrations. Using a Markov-chain model, a formal link between the LPD and the thermodynamic free energy is now provided. It is estimated that the free energy required to produce isochromatid breaks or dicentrics is about 3.67 KJ/mole/aberration and 18.4 KJ/mole, in good agreement with free energy estimates on the formation of DNA.     

科尔沁沙地盐生草甸主要植物群落种群格局的研究

本文采用方差/均值法,Greig-Smith格局分析法及Hill格局分析法,探讨了科尔沁沙地盐生草甸主要植物群落种群格局及其成因。结果表明,羊草群落和野古草群落中的大部分种为聚集分布,羊草与野古草群落交错区中所有种为聚集分布,其最小面积为0.01m~2,最大面积为6.4×6.4m~2。邻接格子最小取样面积应小于0.05×0.05m~2,最适取样面积为40.96m~2,小规模格局是种子扩散和营养繁殖的结果,中规模起因于匍匐和长根茎的扩散,大规模则取决于土壤总盐分及pH值。     

A comparison of methods for detecting bacteriophage contamination of tissue culture sera

Summary Detection of bacteriophage contamination of tissue culture sera by direct plating has been compared with detection methods based on batch enrichment and on the Poisson distribution (PD plating). Batch enrichment is extremely sensitive for detecting the presence of phage contamination. PD plating combines sensitive, withy isolation of each contaminating phage in pure culture. Both batch enrichment and PD plating are more sensitive than direct plating. Neither method requires highly trained personnel or specialized equipment.     

Spatial event cluster detection using a compound Poisson distribution

Geographic disease surveillance methods identify regions that have higher disease rates than expected. These approaches are generally applied to incident or prevalent cases of disease. In some contexts, disease-related events rather than individuals are the appropriate units of analysis for geographic surveillance. We propose a compound Poisson approach that detects event clusters by testing individual areas that may be combined with their nearest neighbors. The method is applicable to situations where the population sizes are diverse and the population distribution by important strata may differ by area. For example, a geographical region might have sparse population in the northern areas, and other areas which are predominantly retirement communities. The approach requires a coarse geographical relationship and administrative data for the numbers of population, cases, and events in each area. Pediatric self-inflicted injuries requiring presentation to Alberta emergency departments provide an illustration.     

Statistical Significance of Mutation Frequencies,and the Power of Statistical Testing,Using the Poisson Distribution

The Poisson distribution may be employed to test whether mutation frequencies differ from control frequencies. This paper describes how this testing procedure may be used for either one-tailed or two-tailed hypotheses. It is also shown how the power of the statistical test can be calculated, the power being the probability of correctly concluding the null hypothesis to be false.     

Sample size calculations for noninferiority trials with Poisson distributed count data

Clinical trials with Poisson distributed count data as the primary outcome are common in various medical areas such as relapse counts in multiple sclerosis trials or the number of attacks in trials for the treatment of migraine. In this article, we present approximate sample size formulae for testing noninferiority using asymptotic tests which are based on restricted or unrestricted maximum likelihood estimators of the Poisson rates. The Poisson outcomes are allowed to be observed for unequal follow‐up schemes, and both the situations that the noninferiority margin is expressed in terms of the difference and the ratio are considered. The exact type I error rates and powers of these tests are evaluated and the accuracy of the approximate sample size formulae is examined. The test statistic using the restricted maximum likelihood estimators (for the difference test problem) and the test statistic that is based on the logarithmic transformation and employs the maximum likelihood estimators (for the ratio test problem) show favorable type I error control and can be recommended for practical application. The approximate sample size formulae show high accuracy even for small sample sizes and provide power values identical or close to the aspired ones. The methods are illustrated by a clinical trial example from anesthesia.     

Various X2-Tests of Homogeneity: Some Comments

Methodological issues in the analysis of incidence rates or prevalence proportions for count data, presented in a form of a sequence of 2×2 tables, corresponding to levels (strata) of a specified variable (risk factor) X, are discussed. Suppose λ_1i and λ_2i are the incidence rates of an event D in the ith stratum for populations 1 and 2, respectively. The homogeneity (null) hypothesis is formulated in the form: H_0:λ1i=λ_2i for all i (i = 1, 2, …, I). Three X²-tests for H₀ and their theoretical bases are discussed: X_Total² which is sensitive to alternatives HA :λ1i± λ2i for at least some i; X_Comb² which is sensitive to alternatives H A : λ1iλ2i² or < λ_2i but not both for all i; and X_Diff² which is sensitive to alternatives H_A:λ1i>λ2i³ for some i and λ_1i′ < λ_2i′ for some i′ (i≠i′). These statistics satisfy the relation X_Total² = X_Comb² + X_Diff². Also, X′²-statistic for pooled data is calculated, which in conjunction with X_Comb² can serve for detecting confounding. Although most of these techniques are known, they are rather scattered in the literature, and not always considered jointly, as it is emphasized in the present paper. It is hoped that these comments will be helpful to biostatisticians as well as to epidemiologists and medical researchers in the analysis of mortality and morbidity data. For illustration, two examples with large sets of epidemiological data are given.     

Bivariate ZIP Models

The Zero‐Inflated Poisson model is extended into a bivariate form. Three new bivariate models are considered. Parameters are estimated by maximum likelihood. Two numerical examples are discussed.     

Extinction times and moment closure in the stochastic logistic process

We investigate the statistics of extinction times for an isolated population, with an initially modest number M of individuals, whose dynamics are controlled by a stochastic logistic process (SLP). The coefficient of variation in the extinction time V is found to have a maximum value when the death and birth rates are close in value. For large habitat size K we find that Vmax is of order K1/4 / M1/2, which is much larger than unity so long as M is small compared to K1/2. We also present a study of the SLP using the moment closure approximation (MCA), and discuss the successes and failures of this method. Regarding the former, the MCA yields a steady-state distribution for the population when the death rate is low. Although not correct for the SLP model, the first three moments of this distribution coincide with those calculated exactly for an adjusted SLP in which extinction is forbidden. These exact calculations also pinpoint the breakdown of the MCA as the death rate is increased.     

Computer simulation of error rates of Poisson-based interval estimates of plankton abundance

The routine assignment of error rates (confidence intervals) to Poisson distribution estimates of plankton abundance should be rejected. In addition to the interval estimation procedure being pseudoreplicative, it is not robust to common violations of its assumptions. Because the spatial dispersion of organisms in sampling units from the counting chamber to the field is rarely random and because counting protocols are usually terminated by a count threshold having been equalled or exceeded, Poisson based estimates are usually derived from sampling non-Poisson distributions. Computer simulation was used to investigate the quantitative consequences of such estimates. The expected mean error rate of 95% confidence intervals is inflated from 5% to 15% as contagion increases, as the parametric variance-mean ratio increases from 1 to 2. Also, count threshold termination of the counting protocol effects both a biased estimate of the parametric mean (or total) and alters expected mean error rates, especially if the total count is low (< 100 organisms) and the mean density in the sampling unit is low.     

Extended Poisson Process Modelling and Analysis of Count Data

It is shown that any discrete distribution with non-negative support has a representation in terms of an extended Poisson process (or pure birth process). A particular extension of the simple Poisson process is proposed: one that admits a variety of distributions; the equations for such processes may be readily solved numerically. An analytical approximation for the solution is given, leading to approximate mean-variance relationships. The resulting distributions are then applied to analyses of some biological data-sets.     

The distribution of rare alleles

Population geneticists have long been interested in the behavior of rare variants. The definition of a rare variant has been the subject of some debate, centered mainly on whether alleles with small relative frequency should be considered rare, or whether alleles with small numbers should be. We study the behavior of the counts of rare alleles in samples taken from a population genetics model that allows for selection and infinitely-many-alleles mutation structure. We show that in large samples the counts of rare alleles — those represented once, twice, ... — are approximately distributed as a Poisson process, with a parameter that depends on the total mutation rate, but not on the selection parameters. This result is applied to the problem of estimating the fraction of neutral mutations.     

Efficient Simulation of Multivariate Binomial and Poisson Distributions

Power investigations, for example, in statistical procedures for the assessment of agreement among multiple raters often require the simultaneous simulation of several dependent binomial or Poisson distributions to appropriately model the stochastical dependencies between the raters' results. Regarding the rather large dimensions of the random vectors to be generated and the even larger number of interactions to be introduced into the simulation scenarios to determine all necessary information on their distributions' dependence stucture, one needs efficient and fast algorithms for the simulation of multivariate Poisson and binomial distributions. Therefore two equivalent models for the multivariate Poisson distribution are combined to obtain an algorithm for the quick implementation of its multivariate dependence structure. Simulation of the multivariate Poisson distribution then becomes feasible by first generating and then convoluting independent univariate Poisson variates with appropriate expectations. The latter can be computed via linear recursion formulae. Similar means for simulation are also considered for the binomial setting. In this scenario it turns out, however, that exact computation of the probability function is even easier to perform; therefore corresponding linear recursion formulae for the point probabilities of multivariate binomial distributions are presented, which only require information about the index parameter and the (simultaneous) success probabilities, that is the multivariate dependence structure among the binomial marginals.     

Effect of Fruiting Traits on the Field Resistance of Cocoa (Theobroma cacao L.) Clones to Phytophthora megakarya

The effects of some traits of field resistance (precocity and duration of the fruiting cycle, age of diseased fruit and vertical pod distribution on the tree) to Phytophthora megakarya of four known cocoa clones were studied in an on‐station clonal plot planted in 1982 in the south‐west of Cameroon. Weekly observations of fruit set and development, black pod and rainfall were carried out during three growing seasons (1999, 2000 and 2001). The study confirmed the previous field and laboratory assessments of resistance of these clones based on the mean percentages of rotten pods obtained annually. The present study has permitted the identification of fruit aged 2–3 months as the highly susceptible stage of development in the most susceptible clone. In addition, precocity and pod cycle duration varied significantly among the clones. The earlier the pod cycle began, the more susceptible was the clone: the most resistant clone started flowering 1 month after the most susceptible clone and therefore escaped the peak of disease severity. Rainfall intensity greatly modified the incidence of the disease in 2001, with high yield losses occurring in all four clones (70–93%), but their ranking remained stable over the 3 years. The spatial distribution of pods on the trees showed that pods on the trunk were more likely to become diseased than those on the branches, but its effect as a clone resistance component is variable among the four clones; the resistant clone producing more pods on the trunk and the susceptible clone more in the canopy.