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- In probability theory, the stable count distribution is the conjugate prior of a one-sided stable distribution. This distribution was discovered by Stephen Lihn (Chinese: 藺鴻圖) in his 2017 study of daily distributions of the S&P 500 and the VIX. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the three parameters defining the distribution, the stability parameter is most important. Stable count distributions have . The known analytical case of is related to the VIX distribution (See Section 7 of ). All the moments are finite for the distribution. (en)
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- 27366 (xsd:nonNegativeInteger)
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- integral form exists (en)
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- not analytically expressible (en)
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- Fox-Wright representation exists (en)
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- not analytically expressible (en)
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- ∈ — location parameter (en)
- ∈ — scale parameter (en)
- ∈ — stability parameter (en)
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- x ∈ R and x ∈ [\nu_0, ∞)|pdf=] (en)
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| rdfs:comment
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- In probability theory, the stable count distribution is the conjugate prior of a one-sided stable distribution. This distribution was discovered by Stephen Lihn (Chinese: 藺鴻圖) in his 2017 study of daily distributions of the S&P 500 and the VIX. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. (en)
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- Stable count distribution (en)
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