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For sufficiently large values of λ, (say λ >1000), the normal distribution with mean λ and variance λ (standard deviation ) is an excellent approximation to the Poisson distribution. If λ is greater than about 10, then the normal distribution is a good approximation if an appropriate continuity correction is performed, i.e., if P( X ≤ x ...
A continuity correction can also be applied when other discrete distributions supported on the integers are approximated by the normal distribution. For example, if X has a Poisson distribution with expected value λ then the variance of X is also λ, and = (< +) (+ /)
The Poisson distribution, which describes a very large number of individually unlikely events that happen in a certain time interval. Related to this distribution are a number of other distributions: the displaced Poisson, the hyper-Poisson, the general Poisson binomial and the Poisson type distributions.
If X 1 is a normal (μ 1, σ 2 1) random variable and X 2 is a normal (μ 2, σ 2 2) random variable, then X 1 + X 2 is a normal (μ 1 + μ 2, σ 2 1 + σ 2 2) random variable. The sum of N chi-squared (1) random variables has a chi-squared distribution with N degrees of freedom. Other distributions are not closed under convolution, but their ...
In statistics, the concept of the shape of a probability distribution arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population.
The (a,b,0) class of distributions is also known as the Panjer, [1] [2] the Poisson-type or the Katz family of distributions, [3] [4] and may be retrieved through the Conway–Maxwell–Poisson distribution. Only the Poisson, binomial and negative binomial distributions satisfy the full form of this
In probability theory, the law of rare events or Poisson limit theorem states that the Poisson distribution may be used as an approximation to the binomial distribution, under certain conditions. [1] The theorem was named after Siméon Denis Poisson (1781–1840). A generalization of this theorem is Le Cam's theorem
Normal probability plots are made of raw data, residuals from model fits, and estimated parameters. A normal probability plot. In a normal probability plot (also called a "normal plot"), the sorted data are plotted vs. values selected to make the resulting image look close to a straight line if the data are approximately normally distributed.