Definition
A discrete stochastic variable X is said to have a Poisson distribution with parameter λ>0, if for k = 0, 1, 2, ... the probability mass function of X is given by:
where
- e is the base of the natural logarithm (e = 2.71828...)
- k! is the factorial of k.
The positive real number λ is equal to the expected value of X, but also to the variance:
The Poisson distribution can be applied to systems with a large number of possible events, each of which is rare. The Poisson distribution is sometimes called a Poissonian.
Read more about this topic: Poisson Distribution
Famous quotes containing the word definition:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)