# binomial distribution

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Related to binomial distributions: Normal distributions, Poisson distributions

## bi·no·mi·al dis·tri·bu·tion

1. a probability distribution associated with two mutually exclusive outcomes, for example, presence or absence of a clinical sign.
2. the possible array of the number of successes in the outcomes from a fixed number, n, of independent Bernoulli trials; the probabilities associated with each constitute a binomial process of order n.

## binomial distribution

The outcomes of a binomial experiment with their corresponding discrete probability distribution.

## Ber·noul·li dis·tri·bu·tion

(ber-nū'lē dis'tri-byū'shŭn)
Probability distribution that describes likelihood of various combinations of two alternate outcomes in a series of independent trials.
Synonym(s): binomial distribution.
[Jakob Bernoulli, 1654-1705, Swiss mathematician]

## binomial

composed of two terms, e.g. names of organisms formed by combination of genus and species names.

binomial distribution
categorization of a group into two mutually exclusive subgroups, e.g. sick and not sick.
binomial population
a population which can be divided into a binomial distribution.

## distribution

the arrangement of numerical data. The arrangement may be in accordance with magnitude, a frequency distribution, or in relation to geographical location, a spatial distribution.

age distribution
see age distribution.
bimodal distribution
the distribution has two regions of high frequency of observations separated by a zone of low frequency.
binomial distribution
a probability distribution associated with two mutually exclusive outcomes.
cluster distribution
a nonrandom distribution with observations aggregating about geographic or temporal variables. May be deceptive and merely reflect the distribution of an uneven population.
frequency distribution
a table or graph of the frequency of occurrence of each value of a variable.
Gaussian distribution
see normal distribution (below).
hypergeometric distribution
may apply to sampling without replacement of a finite population.
lognormal distribution
a distribution which is normal when the log values of the variable are considered.
normal distribution
a graph of the distribution appears as a bell-shaped curve which is symmetrical on the two sides of the vertical axis through the peak of the curve. Called also gaussian distribution.
parent distribution
the distribution (population) that was originally sampled.
Poisson distribution
regular distribution
distributed at regular intervals of time or space; all values within its given interval are equally likely.
sex distribution
an increase in frequency in one sex, which includes neutered males and neutered females. Called also sex-linked or sex-associated.
skewed distribution
a distribution in which the curve illustrating it is not symmetrical but has a long tail on one or other side of the graph.
spatial distribution
variations in distribution related to position in space, e.g. close to the door of a barn.
t-distribution
see t-test.
temporal distribution
variation in distribution related to time, e.g. occurrence of disease incidents after visits by veterinarians, inseminators, feed salesmen.
References in periodicals archive ?
Vanasse, 1989, A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with Regression Component, ASTIN Bulletin, 19: 199-212.
Smith (1999) modeled angling success for salmon, expressed as the catch after the first hour of angling, using a negative binomial distribution model.
The binomial distribution is a discrete frequency (probability) distribution of the number of times an event occurs in a sample in which some proportion of the members possess some variable attribute (Snedecor and Cochran, 1967).
A negative binomial distribution will converge to a Poisson as the variance approaches the mean (Bliss and Fisher, 1953).
A logistic link function was used under the binomial distribution assumption applied for the probability of positive catch component in the delta-lognormal and delta-Poisson model approaches.
Modeled in this way, the negative binomial model is expected to provide year-effect coefficients very close in absolute value to the unstandardized, mean simulated catch per trip of the true underlying negative binomial distribution because no other classification effects are present to account for variance from the unstandardized mean.
0, which was also the expected result given the true negative binomial distribution of the simulated data (SAS, 2000).
The consequence of assuming a lognormal model for the true underlying negative binomial distribution was a more extreme smoothing of the true time series trends than with the other model assumptions, with a decline of only 28% over the time series (Fig.
The dispersion estimate indicated some overdispersion of the data with respect to the binomial distribution (Table 10).
The present study indicates that MRFSS catch rates generally are not normally or lognormally distributed but usually best characterized by the Poisson or negative binomial distribution, depending on the manner in which the catch rate is configured.
Tests of significance were based on the [chi square] statistic for the binomial distribution of the proportion of positive tows (McCullagh and Nelder, 1989).
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