Poisson Distribution

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Related to Poisson random variable: Exponential random variable, Hypergeometric random variable

Poisson Distribution

In statistics, a distribution representing the probability of a random event that occurs at regular intervals on average. Each event occurs independently of every other one.
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References in periodicals archive ?
Corcino, "The generalized factorial moments in terms of a poisson random variable," Journal of Mathematics, Statistics & Operations Research, vol.
We focused on the model involving two independent Poisson random variables since this is a case where the distribution of the MLE is not easily derivable and exact CIs cannot be built; thus, transformation of the estimates is a viable tool to refine the standard naive interval estimator derived by the central limit theorem.
It seems reasonable, therefore, for all [lambda] > 7.84 = [(2.8).sup.2] to use the central limit theorem approximation when simulating a realization of a Poisson random variable. When simulating realizations of many Poisson random variables, it is most efficient to use the normal approximation whenever it is reasonable, because each realization requires only one call to a procedure for simulating a realization of a standard normal random variable.
Throughout this section, without any other specification, the number M of planes is assumed to be a Poisson random variable, so that Eq.
If p = c/2n and c < 1 is constant, then [N.sub.n] converges weakly to N = [2.sup.[PSI]] where [PSI] is a Poisson random variable with mean
where [N.sub.i] is a Poisson random variable that represents the number of claims that have occurred for the client i and [X.sub.i1], ..., [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are independent identically distributed Gamma random variables (continuous variables).
Therefore, when the zero-truncated Poisson random variable X has the same mean as that of its mixture Y, then there is no simple stochastic ordering between X and Y.