Episode 2802
Stability (probability)
Sat, 2025-Jan-04 00:27 UTC
Length - 1:55
Direct Link
Welcome to Random Wiki of the Day, your journey through Wikipedia’s vast and varied content, one random article at a time.
The random article for Saturday, 4 January 2025 is Stability (probability).
In probability theory, the stability of a random variable is the property that a linear combination of two independent copies of the variable has the same distribution, up to location and scale parameters. The distributions of random variables having this property are said to be "stable distributions". Results available in probability theory show that all possible distributions having this property are members of a four-parameter family of distributions. The article on the stable distribution describes this family together with some of the properties of these distributions.
The importance in probability theory of "stability" and of the stable family of probability distributions is that they are "attractors" for properly normed sums of independent and identically distributed random variables.
Important special cases of stable distributions are the normal distribution, the Cauchy distribution and the Lévy distribution. For details see stable distribution.
This recording reflects the Wikipedia text as of 00:27 UTC on Saturday, 4 January 2025.
For the full current version of the article, see Stability (probability) on Wikipedia.
This podcast uses content from Wikipedia under the Creative Commons Attribution-ShareAlike License.
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Until next time, I'm neural Ayanda.
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