# 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 ?
The range of probabilities of negative binomial distribution is obtained using the following calculation (JOHNSON and KOTZ, 1969):
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.
For this reason, the negative binomial distribution (nbd) was deemed more appropriate than Poisson.
is the probability function of a negative binomial distribution with parameters equal to
To isolate the consequences of possible model misspecification in deriving standardized indices of abundance, negative binomial distributions with characteristics like those of MRFSS recreational catch-per-trip distributions were simulated by using the SAS RANTBL function (SAS, 2000).
In particular, Johnson and Kotz (1969) pointed out, "The negative binomial distribution is very often a first choice as alternative when it is felt that a Poisson distribution might be inadequate" (p.
Second, perhaps the available sample sizes simply provide insufficient statistical power to detect deviations from a binomial distribution of the magnitude that may be occurring in the study population.
Chi-square tests in Table 1 indicate that greater disparities between the observed tree seedling distribution, and its random expectations generated by either the Poisson or the binomial distributions, are to be expected more than 90 times in 100 by chance alone.
Counts of biological populations often are fitted well by the negative binomial distribution (Anscombe 1949, Bliss and Fisher 1953, Bowden et al.
The first term in Equation 4 is E(k), which, for the binomial distribution, is n[p.
Computer methods for sampling from gamma, beta, poisson and binomial distributions, Computing 12, (1974), 223-246.
html) , fitting a binomial model to these distributions, and predicting operational false accept performance from the "best fit" binomial distributions.
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