Wiktionary
n. (context statistics English) The discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p.
WordNet
n. a theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success [syn: Bernoulli distribution]
Wikipedia
| kurtosis = $\frac{1-6p(1-p)}{np(1-p)}$
| entropy = $\frac12 \log_2 \big( 2\pi e\, np(1-p) \big) + O \left( \frac{1}{n} \right)$
in shannons. For nats, use the natural log in the log.
| mgf = (1 − p + pe)
| char = (1 − p + pe)
| pgf = G(z) = [(1 − p) + pz].
| fisher = $g_n(p) = \frac{n}{p(1-p)}$
(for fixed n)
}}
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. A success/failure experiment is also called a Bernoulli experiment or Bernoulli trial; when n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one. However, for N much larger than n, the binomial distribution is a good approximation, and widely used.
Usage examples of "binomial distribution".
Bernoulli's Theorem, the Bayes-Laplace theorem, the Poisson Distribution, Negative Binomial Distribution .
Suffice it that Poisson was a mathematician and that Poisson's frequency distribution is a good approximation to the binomial distribution as the number of trials increases and probability of success in a single trial is small.
It was full of numbers: a table for binomial distribution of coin-tossing probabilities, with x as the probability of throwing n heads, divided by the probability of throwing an equal number of heads and tails.