Stable Distribution
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In probability theory, a random variable is said to be stable (or to have a stable distribution) if it has the property that a linear combination of two Independence (probability theory)|independent copies of the variable has the same probability distribution|distribution, up to location parameter|location and scale parameter|scale parameters. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution. The importance of stable probability distributions is that they are attractors for properly normed sums of independent and identically-distributed (iid) random variables. The normal distribution is one family of stable distributions. By the classical central limit theorem the properly normed sum of a set of random variables, each with finite variance, will tend towards a normal distribution as the number of variables increases. Without the finite variance assumption the limit may be a stable distribution. Stable distributions that are non-normal ...
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