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At least 19 recordsLinked to original sources
PubMed2005

Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution.

We prove that the generalized Poisson distribution GP(theta, eta) (eta > or = 0) is a mixture of Poisson distributions; this is a new property for a distribution which is the topic of the book by Consul (1989). Because we find that the fits to count data of the generalized Poisson and negative binomial distributions are often similar, to understand their differences, we compare the probability mass functions and skewnesses of the generalized Poisson and negative binomial distributions with the first two moments fixed. They have slight differences in many situations, but their zero-inflated distributions, with masses at zero, means and variances fixed, can differ more. These probabilistic comparisons are helpful in selecting a better fitting distribution for modelling count data with long right tails. Through a real example of count data with large zero fraction, we illustrate how the generalized Poisson and negative binomial distributions as well as their zero-inflated distributions can be discriminated.

Binomial Distribution↗
PubMed1988

[An analysis of transmission in the interneuronal synapses using a convolution of binomial distributions].

The convolution of two binomial distributions has been used for the analysis of the discrete distributions of the elementary EPSPs amplitude in the sensorimotor, proprio- and reticulo-motoneuronal synapses of the frog. It is shown that the quantity of the working transmitter release sites is higher than that estimated by the binomial distribution. The probability of the release sites response to the single action potential was unequal. In most sites they did not exceed 0.1-0.3 and were supported on the constant level. The effect on the transmitter release mechanism induced blocking of the release sites. The disturbance of preparation to the transmitter release sharply decreased the probability of the release sites response.

Animals↗
PubMed2005

Binomial distribution sample confidence intervals estimation for positive and negative likelihood ratio medical key parameters.

Likelihood Ratio medical key parameters calculated on categorical results from diagnostic tests are usually express accompanied with their confidence intervals, computed using the normal distribution approximation of binomial distribution. The approximation creates known anomalies,especially for limit cases. In order to improve the quality of estimation, four new methods (called here RPAC, RPAC0, RPAC1, and RPAC2) were developed and compared with the classical method (called here RPWald), using an exact probability calculation algorithm.Computer implementations of the methods use the PHP language. We defined and implemented the functions of the four new methods and the five criterions of confidence interval assessment. The experiments run for samples sizes which vary in 14 - 34 range, 90 - 100 range (0 < X < m, 0< Y < n), as well as for random numbers for samples sizes (4m, n </= 1000) and binomial variables (1 </= X, Y < m, n). The experiment run shows that the new proposed RPAC2 method obtains the best overall performance of computing confidence interval for positive and negative likelihood ratios.

Algorithms↗
PubMed2005

Modelling macroparasite aggregation using a nematode-sheep system: the Weibull distribution as an alternative to the negative binomial distribution?

Macroparasites are almost always aggregated across their host populations, hence the Negative Binomial Distribution (NBD) with its exponent parameter k is widely used for modelling, quantifying or analysing parasite distributions. However, many studies have pointed out some drawbacks in the use of the NBD, with respect to the sensitivity of k to the mean number of parasites per host or the under-representation of the heavily infected hosts in the estimate of k. In this study, we compare the fit of the NBD with 4 other widely used distributions on observed parasitic gastrointestinal nematode distributions in their sheep host populations (11 datasets). Distributions were fitted to observed data using maximum likelihood estimator and the best fits were selected using the Akaike's Information Criterion (AIC). A simulation study was also conducted in order to assess the possible bias in parameter estimations especially in the case of small sample sizes. We found that the NBD is seldom the best fit for gastrointestinal nematode distributions. The Weibull distribution was clearly more appropriate over a very wide range of degrees of aggregation, mainly because it was more flexible in fitting the heavily infected hosts. Moreover, the Weibull distribution estimates are less sensitive to sample size. Thus, when possible, we suggest to carefully check on observed data if the NBD is appropriate before conducting any further analysis on parasite distributions.

Animals↗
PubMed1987

A stabilized moment estimator for the beta-binomial distribution.

The beta-binomial distribution has been proposed as a model for the incorporation of historical control data in the analysis of rodent carcinogenesis bioassays. Low spontaneous tumor incidences along with the small number and sizes of historical control groups combine to make the moment and maximum likelihood estimates of the beta-binomial parameters deficient. We therefore propose a stabilized moment estimator for one of the parameters. The stabilized moment estimator is similar to the ridge regression estimator and introduces a shrinkage parameter. Computer simulations were run to examine the behavior of the stabilized moment estimator. The effect of the stabilized moment estimator on the score test for dose-related trend is considered both on simulated data and on an example from the literature.

Animals↗
PubMed1993

Does the negative binomial distribution add up?

The negative binomial distribution (NBD) is widely used to describe the distribution of parasitic helminths in a number of host individuals and has proved a useful, though possibly overused, empirical and theoretical device. It is therefore important that the limits to the applicability of the NBD be clearly defined. In this paper, Alan Grafen and Mark Woolhouse consider applications of the NBD in situations where either the host or parasite population can be divided into subpopulations of different types (eg. by age, sex or genotype), and they describe the relationships between the frequency distributions relevant to the different subpopulations and those relevant to the total population.

Journal Article↗
PubMed2001

Using the binomial distribution to assess effort: forced-choice testing in neuropsychological settings.

The binomial distribution is often, but prematurely, rejected as a tool for assessing effort. This study extended previous research using published clinical and computer-generated pseudo subject data for the Test of Memory Malingering (TOMM). The efficiencies of eight cut points based upon inverse binomial distribution functions were compared with the cut point recommended in the test manual for making correct classifications, and a new statistic, the total number of errors, was also compared with the test manual cut point. Repeated measures, multivariate, and univariate ANOVAs, Bonferroni-corrected post-hoc t-tests, and normal curve density functions were employed to assess the homogeneity of groups within experimental conditions. Based upon these analyses, changes were recommended in the decision rules for the TOMM, and strategies for improving the norms for the TOMM and for neuropsychological assessment instruments, generally, were discussed.

Binomial Distribution↗
PubMed2007

Analysis of the short form-36 (SF-36): the beta-binomial distribution approach.

Health-related quality of life (HRQoL) is an important indicator of health status and the Short Form-36 (SF-36) is a generic instrument to measure it. Multiple linear regression (MLR) is often used to study the relationship of HRQoL with patients' characteristics, though HRQoL outcomes tend to be not normally distributed, skewed and bounded (e.g. between 0 and 100). A sample of 193 patients with eating disorders has been analysed to assess the performance of the MLR under non-normality conditions. Normal distribution was rejected for seven out of the eight domains. A beta-binomial distribution is suggested to fit the SF-36 scores. The beta-binomial distribution is not rejected for five out of the eight domains. Thus, a beta-binomial regression (BBR) is suggested to analyse the SF-36 scores. Results using MLR and BBR have been compared for real and simulated data. Performance of the BBR is shown to be better than MLR in the HRQoL domains with few ordered categories and very similar to MLR in the more continuous domains. Moreover, the interpretation of the estimates obtained with BBR is clinically more meaningful. A common technique of statistical analysis is preferable for all the HRQoL dimensions. Therefore, the BBR approach is recommended not only to detect significant predictors of HRQoL when SF-36 is used, but also to analyse and interpret the effect of several explanatory variables on HRQoL. Further work is required to test the better performance of BBR against standard methods for other HRQoL outcomes, populations or interventions.

Adolescent↗
PubMed1996

[Negative binomial distribution of eggs of Schistosoma japonicum in stool].

To understand the nature of distribution of schistosoma japonicum (S. japonicum) eggs in stool of the infected individuals, it is assumed that if regression coefficient b approaches two in the equation lg (v) = a + blg(m), with a larger mean of egg counts (m), they can be considered compatible with negative binomial distribution. Results of this study showed egg counts of S. japonicum in stool of the same infected individual on different days and in male and female population can be described by negative binomial distribution, with 95 percent confidence intervals of coefficient of regression 1.3006-2.2956, 1.6109-1.9703, 1.7060-2.1589, and 1.5507-2.2359, respectively. Goodness of fit tests for the observed data indicated that fitting for negative binomial distribution was good. It suggests that the method of moments (coefficient of regression) can be used to determine whether the observed distribution of frequencies is compatible with a negative binomial one.

Animals↗
PubMed2005

Binomial distribution based tau-leap accelerated stochastic simulation.

Recently, Gillespie introduced the tau-leap approximate, accelerated stochastic Monte Carlo method for well-mixed reacting systems [J. Chem. Phys. 115, 1716 (2001)]. In each time increment of that method, one executes a number of reaction events, selected randomly from a Poisson distribution, to enable simulation of long times. Here we introduce a binomial distribution tau-leap algorithm (abbreviated as BD-tau method). This method combines the bounded nature of the binomial distribution variable with the limiting reactant and constrained firing concepts to avoid negative populations encountered in the original tau-leap method of Gillespie for large time increments, and thus conserve mass. Simulations using prototype reaction networks show that the BD-tau method is more accurate than the original method for comparable coarse-graining in time.

Journal Article↗
PubMed2005

Statistical motor number estimation assuming a binomial distribution.

The statistical method of motor unit number estimation (MUNE) uses the natural stochastic variation in a muscle's compound response to electrical stimulation to obtain an estimate of the number of recruitable motor units. The current method assumes that this variation follows a Poisson distribution. We present an alternative that instead assumes a binomial distribution. Results of computer simulations and of a pilot study on 19 healthy subjects showed that the binomial MUNE values are considerably higher than those of the Poisson method, and in better agreement with the results of other MUNE techniques. In addition, simulation results predict that the performance in patients with severe motor unit loss will be better for the binomial than Poisson method. The adapted method remains closer to physiology, because it can accommodate the increase in activation probability that results from rising stimulus intensity. It does not need recording windows as used with the Poisson method, and is therefore less user-dependent and more objective and quicker in its operation. For these reasons, we believe that the proposed modifications may lead to significant improvements in the statistical MUNE technique.

Adult↗
PubMed2026

SNP genotyping in Pseudotsuga menziesii and Pinus radiata using targeted genotyping-by-sequencing (GBS): improved Bayesian SNP calling using a beta-binomial distribution and other optimized input parameters.

BACKGROUND: Single-nucleotide polymorphism markers (SNPs) have important applications in gene conservation, breeding, and fundamental genetics research. Our long-term goal is to develop routine approaches for SNP genotyping in forest trees. Ideally, these approaches would be inexpensive, able to accommodate a wide range of samples and SNPs, available through commercial providers, and produce high-quality SNP data. RESULTS: Using targeted genotyping-by-sequencing (GBS), we developed SNP assays for two highly heterozygous tree species, Douglas-fir (Pseudotsuga menziesii) and radiata pine (Pinus radiata). Using Douglas-fir haploid and diploid data, we optimized Bayesian SNP calling by testing four input parameters: (1) allele and genotype prior probabilities, (2) Rho, the beta-binomial dispersion parameter, (3) estimated read error (BayesReadError), and (4) the logPO cutoff used to filter low confidence SNP calls. logPO is the Bayesian posterior odds ratio for a called SNP. Compared to assuming a binomial distribution of read counts (Rho&#x2009;=&#x2009;0), the beta-binomial distribution (Rho&#x2009;=&#x2009;0.33) substantially reduced call error and heterozygote undercalling. Compared to the other Bayesian parameters, genotype priors had little effect on genotyping success. For Douglas-fir, we tested 5,360 SNP assays, and then studied the performance of the best 4,000. For radiata pine, we tested 6,000 SNP assays, and then studied the performance of the best 4,570. In Douglas-fir and radiata pine, our Bayesian approach resulted in median call rates of 95% to 98% for the top-ranked SNPs, with an estimated call error of 1.60% for known homozygous genotypes and 2.27% for known heterozygotes. In radiata pine, median and mean call rates were above 91% for GBS and SNP genotyping using an Axiom fixed genotyping array. Additionally, the median correspondence between the GBS and Axiom genotypes was about 98% overall (mean 96%). CONCLUSIONS: By optimizing Bayesian SNP calling, selecting the best 4-5&#xa0;K SNPs, and excluding samples with low DNA amounts, we substantially reduced call error and heterozygote undercalling, resulting in SNP genotypes that were nearly identical to genotypes obtained using the Axiom array. Furthermore, genotyping performance should increase even further if our SNP rankings were used to develop less complex probe pools that target fewer SNPs.

Pinus↗
PubMed1981

Bacterial density in water determined by poisson or negative binomial distributions.

The question of how to characterize the bacterial density in a body of water when data are available as counts from a number of small-volume samples was examined for cases where either the Poisson or negative binomial probability distributions could be used to describe the bacteriological data. The suitability of the Poisson distribution when replicate analyses were performed under carefully controlled conditions and of the negative binomial distribution for samples collected from different locations and over time were illustrated by two examples. In cases where the negative binomial distribution was appropriate, a procedure was given for characterizing the variability by dividing the bacterial counts into homogeneous groups. The usefulness of this procedure was illustrated for the second example based on survey data for Lake Erie. A further illustration of the difference between results based on the Poisson and negative binomial distributions was given by calculating the probability of obtaining all samples sterile, assuming various bacterial densities and sample sizes.

Journal Article↗
PubMedDate not supplied

[Negative binomial distribution versus Poisson in the analysis of recurrent phenomena].

OBJECTIVE: The aim is to unfold the difficulties likely to arise in risk calculations through aggregated database when the studied phenomenon is recurrent and to display the negative binomial distribution as a valid and simple alternative to analyse this kind of phenomenon. METHODS: When the studied phenomenon is recurrent, the analysis by means of the Poisson regression can provoke overdispersion or extra-poisson variance, what leads to underestimating the standard errors in coefficients and may divert into the statistical significance of factors which as a matter of fact are not associated with the phenomenon beforehand. The negative binomial can grasp part of the variance which the Poisson is unable to identify. In order to check this out, the fit of both distributions were compared, based on the number of hospitalizations of individuals aged between 65 and 69, during 1996. This comparison was carried out by means of two different aggregated databases: by individuals and by variables. RESULTS: There were differences in the fitted models by means of both distributions in both databases. By the analysis of the residuals, when using the base by individuals, the negative binomial fits correctly 67.9% of the observations badly fitted by the Poisson. Using the aggregated variables database, the percentage is 50%. In both cases, Poisson estimates four out of the six studied variables as significant. As to the negative binomial, there are two significant based on individuals and one in the variable database. CONCLUSION: The existence of overdispersion is frequent in recurrent-type phenomena. When this occurs, the negative binomial distribution is more appropiate than the Poisson.

Aged↗
PubMed1988

Fitting of a binomial distribution to the number of chiasmata per bivalent.

Statistical tests on the distribution of the number of chiasmata per chromosome, collected from literatures, showed that they can be approximated by binomial distributions with one obligatory chiasma, i.e., B(N-1, p). N is proportional to the average number of chiasmata, while p is nearly constant for the species tested.

Analysis of Variance↗
PubMed1993

Epidemiologic analyses of spatial clustering of bovine ephemeral fever outbreaks. I. Application of the negative binomial distribution.

An epidemic that propagates through a population results in a contagious spatial pattern. The incidence per farm of bovine ephemeral fever (BEF) outbreaks in the 22 areas of Fukuoka Prefecture in 1988 was well explained by the negative binomial distribution, which is generally considered, as the clustering of the outbreaks. Furthermore, the clustering was analyzed with three categories of vaccination rate (No. 1-40%, and 40-80%). As a result, the no vaccination and high vaccination rate (41-80%) groups tended to shift to similarly the Poisson distribution. It may be speculated that an insufficient vaccination control of the BEF was influenced with the clustering.

Animals↗
PubMed1989

Tutorial on large deviations for the binomial distribution.

We present, in an easy to use form, the large deviation theory of the binomial distribution: how to approximate the probability of k or more successes in n independent trials, each with success probability p, when the specified fraction of successes, a identical to k/n, satisfies 0 less than p less than a less than 1.

Amino Acid Sequence↗