# 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 ?
where k is the k exponent of negative binomial distribution, m is the mean, and P(x) is the probability of x individuals in a sampling unit.
Parameters R and k of the negative binomial distribution are the reproductive number and dispersion parameter, respectively.
This finding was analogous to the work of Pollard et al (1977) when fitting the negative binomial distribution to groups of players.
For insureds who reported at least once, the predictive distribution returns to a standard multivariate negative binomial distribution because the first parts of the numerator and the denominator of Equation (31) fall.
However, the calculated test statistics for the negative binomial distributions were at least an order of magnitude smaller than those for the Poisson and lognormal distributions, suggesting that an underlying negative binomial distribution was much more likely.
In contrast, researchers in other fields have applied the negative binomial distribution on a wide range of topics.
Recording these draws in (say) groups of four, we obtain the binomial distribution (1),
The Poisson distribution assumes spatial independence, whereas this assumption is relaxed with the negative binomial distribution.
2]) by using the equation for the jth moment of a binomial distribution
The inverse transformation of the binomial distribution function can be implemented by using the recursive formula
The Katz family of distributions, which consists of the Poisson, binomial, and negative binomial distributions, forms a simple class with the property of being equi-, under-, or over-dispersed.
The GENMOD algorithm uses maximum-likelihood estimates for assumed binomial distributions, which are unbiased to a first order of approximation (McCullagh and Nelder, 1989)

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