Stability in Probability Theory
There are a number of mathematical results that can be derived for distributions which have the stability property. That is, all possible families of distributions which have the property of being closed under convolution are being considered. It is convenient here to call these stable distributions, without meaning specifically the distribution described in the article named stable distribution, or to say that a distribution is stable if it is assumed that it has the stability property. The following results can be obtained for univariate distributions which are stable.
- Stable distributions are always infinitely divisible.
- All stable distributions are absolutely continuous.
- All stable distributions are unimodal.
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