The phrase "approximation to the binomial" is correct and usable in written English.
It can be used in mathematical or statistical contexts when discussing methods or formulas that estimate or simplify binomial distributions or processes.
Example: "The approximation to the binomial distribution allows for easier calculations in large sample sizes."
Alternatives: "estimate of the binomial" or "binomial approximation".
Individual entries in Table 1 are each based on 1000 simulations, so their confidence limits are approximately ± 2 (on the basis of the normal approximation to the binomial).
The figure illustrates the normal approximation to the binomial distribution with n = 10 and p = 1/2.
An important stochastic process described implicitly in the discussion of the Poisson approximation to the binomial distribution is the Poisson process.
The result is a different kind of approximation to the binomial distribution, called the Poisson distribution (after the French mathematician Siméon-Denis Poisson) or the law of small numbers.
Although originally derived as merely an approximation to the binomial distribution (obtained by repeated, independent trials that have only one of two possible outcomes), the Poisson distribution is now fundamental in the analysis of problems concerning radioactivity, traffic, and the random occurrence of events in time or space.
The normal distribution was first used by de Moivre (1733) in the literature as an approximation to the binomial distribution.
In[14], the authors proposed tag estimation methods on the basis of approximations to the binomial distribution.
The proportion of male births was compared with the expected population mean of 0.515 (106:100 expressed in decimals for calculation purposes equals 106/(100 + 106) = 0.515) (Chahnazarian, 1988) by using the z-approximation to the binomial test.
Probability ranges were obtained by constructing 95% confidence intervals for proportions derived from the literature using normal approximations to the binomial distribution.
Dichotomous data with a binomial distribution (e.g., sensitivity) were transformed to the log odds scale because this scale has a normal distribution and is a good approximation to the exact binomial distribution.
The distribution of the counts Y i is typically assumed to come from a Poisson distribution, as the diseases usually considered in such studies are rare and this distribution gives a good approximation to the underlying binomial distribution that would hold for each risk stratum.
