POISSON DISTRIBUTION TO ANALYZE NEAR-THRESHOLD MOTOR EVOKED POTENTIALS

Motor unit action potentials (MUAPs) evoked by repetitive, low-intensity transcranial magnetic stimulation can be modeled as a Poisson process. A mathematical consequence of such a model is that the ratio of the variance to the mean of the amplitudes of motor evoked potentials (MEPs) should provide an estimate of the mean size of the individual MUAPs that summate to generate each MEP. We found that this is, in fact, the case. Our finding thus supports the use of the Poisson distribution to model MEP generation and indicates that this model enables characterization of the motor unit population that contributes to near-threshold MEPs. Muscle Nerve 42: 825-828, 2010

The zero-inflated Conway-Maxwell-Poisson distribution: Bayesian inference, regression modeling and influence diagnostic

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The exponential COM-Poisson distribution

The Conway-Maxwell Poisson (COMP) distribution as an extension of the Poisson distribution is a popular model for analyzing counting data. For the first time, we introduce a new three parameter distribution, so-called the exponential-Conway-Maxwell Poisson (ECOMP) distribution, that contains as sub-models the exponential-geometric and exponential-Poisson distributions proposed by Adamidis and Loukas (Stat Probab Lett 39:35-42, 1998) and KuAY (Comput Stat Data Anal 51:4497-4509, 2007), respectively. The new density function can be expressed as a mixture of exponential density functions. Expansions for moments, moment generating function and some statistical measures are provided. The density function of the order statistics can also be expressed as a mixture of exponential densities. We derive two formulae for the moments of order statistics. The elements of the observed information matrix are provided. Two applications illustrate the usefulness of the new distribution to analyze positive data.

Statnote 36: Do the data fit the Poisson distribution

In previous Statnotes, many of the statistical tests described rely on the assumption that the data are a random sample from a normal or Gaussian distribution. These include most of the tests in common usage such as the ‘t’ test ), the various types of analysis of variance (ANOVA), and Pearson’s correlation coefficient (‘r’) . In microbiology research, however, not all variables can be assumed to follow a normal distribution. Yeast populations, for example, are a notable feature of freshwater habitats, representatives of over 100 genera having been recorded . Most common are the ‘red yeasts’ such as Rhodotorula, Rhodosporidium, and Sporobolomyces and ‘black yeasts’ such as Aurobasidium pelculans, together with species of Candida. Despite the abundance of genera and species, the overall density of an individual species in freshwater is likely to be low and hence, samples taken from such a population will contain very low numbers of cells. A rare organism living in an aquatic environment may be distributed more or less at random in a volume of water and therefore, samples taken from such an environment may result in counts which are more likely to be distributed according to the Poisson than the normal distribution. The Poisson distribution was named after the French mathematician Siméon Poisson (1781-1840) and has many applications in biology, especially in describing rare or randomly distributed events, e.g., the number of mutations in a given sequence of DNA after exposure to a fixed amount of radiation or the number of cells infected by a virus given a fixed level of exposure. This Statnote describes how to fit the Poisson distribution to counts of yeast cells in samples taken from a freshwater lake.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

The Poisson-exponential distribution: a Bayesian approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. © 2010 Elsevier B.V. All rights reserved.

Control charts for individual observations of a bivariate Poisson process

In this paper, three single-control charts are proposed to monitor individual observations of a bivariate Poisson process. The specified false-alarm risk, their control limits, and ARLs were determined to compare their performances for different types and sizes of shifts. In most of the cases, the single charts presented better performance rather than two separate control charts ( one for each quality characteristic). A numerical example illustrates the proposed control charts.

Destructive weighted Poisson cure rate models

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow a compound weighted Poisson distribution. This model is more flexible in terms of dispersion than the promotion time cure model. Moreover, it gives an interesting and realistic interpretation of the biological mechanism of the occurrence of event of interest as it includes a destructive process of the initial risk factors in a competitive scenario. In other words, what is recorded is only from the undamaged portion of the original number of risk factors.

COM-Poisson cure rate survival models and an application to a cutaneous melanoma data

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow the Conway-Maxwell Poisson distribution. This model includes as special cases some of the well-known cure rate models discussed in the literature. Next, we discuss the maximum likelihood estimation of the parameters of this cure rate survival model. Finally, we illustrate the usefulness of this model by applying it to a real cutaneous melanoma data. (C) 2009 Elsevier B.V. All rights reserved.

Beta-binomial/Poisson regression models for repeated bivariate counts

We analyze data obtained from a study designed to evaluate training effects on the performance of certain motor activities of Parkinson`s disease patients. Maximum likelihood methods were used to fit beta-binomial/Poisson regression models tailored to evaluate the effects of training on the numbers of attempted and successful specified manual movements in 1 min periods, controlling for disease stage and use of the preferred hand. We extend models previously considered by other authors in univariate settings to account for the repeated measures nature of the data. The results suggest that the expected number of attempts and successes increase with training, except for patients with advanced stages of the disease using the non-preferred hand. Copyright (c) 2008 John Wiley & Sons, Ltd.

The Poisson-exponential regression model under different latent activation schemes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Control charts for individual observations of a bivariate Poisson process

In this paper, three single-control charts are proposed to monitor individual observations of a bivariate Poisson process. The specified false-alarm risk, their control limits, and ARLs were determined to compare their performances for different types and sizes of shifts. In most of the cases, the single charts presented better performance rather than two separate control charts ( one for each quality characteristic). A numerical example illustrates the proposed control charts.