Binomial Distribution

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Related to binomial distributions: Normal distributions, Poisson distributions

Binomial Distribution

The distribution of successes and failures of a certain number of Bernoulli trials. A Bernoulli trial is a test in which there are precisely two random outcomes: success and failure. For example, if one is testing whether flipping a coin will result in heads, the two outcomes are yes (success) or no (failure). A binomial distribution, then, would be the number of heads compared to the number of tails in a given number of flips. It is also called a Bernoulli distribution.
References in periodicals archive ?
In our present context, the hypergeometric is, in effect, a binomial distribution with conditional probabilities, indicated by the convention of placing the power n in parentheses, as the power (4) in expansion (2).
One approach to deriving the negative binomial distribution is to assume that the count for each sampling unit is distributed as a Poisson variable with mean [[Mu].
Fishman [16] describes a method for sampling from the binomial distribution by using the acceptance/rejection technique with a uniform majorizing function, and later improves the idea by changing to a Poisson majorizing function [17].
They therefore use the overdispersed negative binomial distribution and anticipate that the negative binomial provides a much better fit in the tail region (see Table 1), an observation confirmed by the Pearson [chi square] test using the parameters based on MLE.
Tests of significance were based on the [chi square] statistic for the binomial distribution of the proportion of positive tows (McCullagh and Nelder, 1989).
The k parameter of the negative binomial distribution estimated by the maximum likelihood method is calculated iteratively and is the value that equates the two members of the following (Bliss and Fisher, 1953):
t] can then actually be obtained by using the relationship between the cumulative beta distribution and the cumulative binomial distribution function as follows (Daly [13] and Johnson et al.
We fit the transmission data from patients within subgroups to the negative binomial distribution with mean R and dispersion parameter k, which characterizes individual variation in transmission, including the likelihood of superspreading events (i.
The parameters a and b of the beta-binomial model can be chosen to provide flexibility to handle many possible situations in health services research that have this "probability" nature of constraining between 0 and 1, and are more diffuse than the over-dispersion capabilities of the negative binomial distribution (Morris and Lock 2009).
Negative binomial distributions were fitted to all pairs of players within a side so that interactions between players could be simulated prior to a match.
The three most common statistical distributions are the normal, Poisson and binomial distributions.