# binomial distribution

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Related to binomial distribution: Poisson distribution, normal distribution

## 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]
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References in periodicals archive ?
In this section, we proposed a new method for odds ratio estimation using Empirical Bayes method in two independent binomial distributions. Let [Y.sub.1] and [Y.sub.2] be random variables, distributed as binomial with equal and unequal sample sizes and unknown probability, [Y.sub.1] ~ Bin ([n.sub.1], [p.sub.1]) and [Y.sub.2] ~ Bin ([n.sub.2], [p.sub.2]), where [n.sub.1], [n.sub.2] and [p.sub.1], [p.sub.2] denote two sample sizes and two unknown success probabilities.
Fact 4 Let X have a binomial distribution. For any 0 [less than or equal to] [delta] [less than or equal to] 1 we have
A recent study (31) produced a similar estimate (k = 0.18; 95% CI 0.10-0.26) when the negative binomial distribution was fitted to data from large Ebola transmission chains in Guinea (32); this result suggests that the high variability assumption may be appropriate, but whether or not the assumption of high variability is an appropriate characterization for potential Ebola outbreaks in new countries is unclear.
If the events are random and not correlated, the distribution of the number of successes is a Binomial distribution. There are many situations where the events are related.
The function argument x=[f.sub.n](y)/[p.sub.n](y) is fixed, where [p.sub.n](y) is the probability for a Binomial distribution, considering the estimate of [pi] given by (4).
Besides, the P value of negative binomial distribution is the largest, which means that negative binomial distribution is able to fit the frequency best.
In Figure 4, the mean system size of System 2 is shown as a function of [eta] when the service time follows the negative binomial distribution.
In statistics, this test is referred to as a "binomial distribution" (25) and is used to determine the probability of obtaining a given number of successes in a fixed number of trials.
The beta-binomial model is a combined model of the beta and binomial distributions. The binomial distribution is a discrete probability distribution arising when the probability of success (p) in each of a fixed or known number of Bernoulli trials (n)is either unknown or random.
The weights present a binomial distribution with the random parameter (2[[beta].sub.p][[lambda].sub.2]).
Exponent k of the negative binomial distribution: the exponent k is a suitable dispersion index when the size and numbers of sample units are the same in each sample, since this is frequently influenced by the size of the sampling units.

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