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PubMed1984

Quantal release of neurotransmitter: an iterative method for the automatic computation of binomial distribution parameters.

A computational method is presented by which, when the amplitude-frequency histogram of the excitatory post-synaptic potentials shows a binomial distribution, an accurate evaluation of the statistical parameters p and n may be obtained. The entire procedure is a combination of 3 basic methods: steepest descent, parabolic interpolation and Montecarlo technique. The two statistical parameters are evaluated independently with respect to each other, which makes an effective control of the accuracy of the calculation possible by comparing the p by n product with the average number of quanta released in response to each nerve impulse, conventionally computed. Applications to quantal release studies in both rat and guinea-pig superior cervical ganglia are also presented.

Animals↗
PubMed2000

Spatial modelling of individual-level parasite counts using the negative binomial distribution.

We present a spatial model for the mean and correlation of highly dispersed count data, and apply it to individual-level counts of the nematode Wuchereria bancrofti, a parasite of humans which causes the disease lymphatic filariasis. Our model uses the negative binomial distribution, whose shape parameter is a convenient index of over-dispersion. Spatial association is quantified in terms of a characteristic length, which has an intuitive interpretation as the distance over which correlation decreases by half. Demographic surveillance and mapping enable us to include individual-level covariates such as age and sex. We discuss the distinctive features of our model and interpret the results in terms of the epidemiology of lymphatic filariasis and possible implications for control programmes.

Journal Article↗
PubMedDate not supplied

The use of the binomial distribution in establishing an association between high-risk donors and transfusion-associated AIDS.

In the first seven cases of transfusion-associated acquired immunodeficiency syndrome (TA-AIDS) with completion of blood donor investigations, there was identification of at least one person (a high-risk donor--HRD) in each donor set who might have transmitted the disease. Using three definitions of an HRD, we estimated the prevalence of HRDs in the overall donor population and used the binomial distribution to calculate the probabilities of finding at least the observed numbers of donor sets with one or more HRDs. These probabilities--0.028, 0.007 and 0.014, respectively--allowed us to reject the null hypothesis that the number of cases of TA-AIDS exposed to an HRD was not greater than that expected by chance, based on the total number of donors to which each case was exposed and the estimated proportion of HRDs in the overall donor population. We concluded that there was a statistically significant association between HRDs and TA-AIDS.

Acquired Immunodeficiency Syndrome↗
PubMed1986

Normal performance variability on a dichotic CV test across nine onset-time-asynchrony conditions: application of a binomial-distribution model.

The purpose of the present study was to generate normative data for a dichotic listening task involving the identification of dichotic consonant vowels at interchannel onset-time asynchronies of 120, 90, 60, 30, and 0 msec, under right- and left-lag conditions. The subjects were 30 healthy young adults, all of whom passed rigorous preliminary testing to ensure normal auditory function. Both group and individual data were analyzed. When the data were collapsed across all subjects, the results were similar to those of previous studies. However, the individual data, analyzed according to a model based on the binomial distribution, demonstrated that the collapsed group data were misleading since they did not predict normal variability. Both the group and the individual results suggested that the 90- and 0-msec conditions are the most useful clinically. Further research involving patients afflicted with lesions, in which the data are gathered and analyzed in a manner similar to that of the present study, was recommended.

Adult↗
PubMed1980

The nonrandom, negative binomial distribution of experimental trichinellosis in rabbits.

The distribution of parasite populations in their hosts has been the subject of a number of mathematical analyses and it has been found that these distributions are generally nonrandom and overdispersed. Data on the recovery of Trichinella spiralis in the laboratory from 371 outbred rabbits were examined. The distribution of their parasite burden was overdispersed and best fit by a negative binomial frequency distribution. The intensity of the infections was almost totally independent of the dose of inoculation, the duration of the infection, and the weight of the animals; the variations within the replicate counts were small and normally distributed about their means. These results indicate that nonrandom overdispersion may be a characteristic of even carefully controlled laboratory infections, and susceptibility factors should be considered seriously in mathematical models of parasites.

Animals↗
PubMed1990

Segregation ratios within Segregation Distorter lines of Drosophila melanogaster conform to a beta-binomial distribution.

Segregation Distorter (SD) chromosomes are preferentially recovered from SD/SD+ males due to the dysfunction of sperm bearing the SD+ chromosome. The proportion of offspring bearing the SD chromosome is given the symbol k. The nature of the frequency distribution of k was examined by comparing observed k distributions produced by six different SD chromosomes, each with a different mean, with k distributions predicted by two different statistical models. The first model was one where the k of all males with a given SD chromosome were considered to be equal prior to the determination of those gametes which produce viable zygotes. In this model the only source of variation of k would be binomial sampling. The results rigorously demonstrated for the first time that the observed k distributions did not fit the prediction that the only source of variation was binomial sampling. The next model tested was that the prior distribution of segregation ratios conformed to a beta distribution, such that the distribution of k would be a beta-binomial distribution. The predicted distributions of this model did not differ significantly from the observed distributions of k in five of the six cases examined. The sixth case probably failed to fit a beta-binomial distribution due to a major segregating modifier. The demonstration that the prior distribution of segregation ratios of SD lines can generally be approximated with a beta distribution is crucial for the biometrical analysis of segregation distortion.

Animals↗
PubMed1993

The binomial distribution and the evidence for independent action of ion channels.

Calculations are presented demonstrating a class of hypothetical channel interactions which cannot be recognized by means of the commonly used binomial test. On the contrary, ion channels which interact in such a way will be identified with the help of the binomial test as independent. Thus, the binomial test cannot be used to prove the absence of interactions. Furthermore, in cases in which existing interactions are recognized by the binomial test, estimation of the strength of the interactions may be inaccurate.

Animals↗