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:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)