Stable count distribution

<p>In <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>, the stable count distribution is the <a href="/facts/Conjugate_prior/ScCFcs8b">conjugate prior</a> of a <a href="/facts/Stable_distribution/rvtRmhlz">one-sided stable distribution</a>. This distribution was discovered by Stephen Lihn (Chinese: 藺鴻圖) in his 2017 study of daily distributions of the <a href="/facts/S%26P_500/oyektBNP">S&P 500</a> and the <a href="/facts/VIX/f3aKRvIR">VIX</a>. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after <a href="/facts/Paul_L%C3%A9vy_(mathematician)/RKFMXMkL">Paul Lévy</a>, the first mathematician to have studied it.
</p><p>Of the three parameters defining the distribution, the stability parameter 
  
    
      
        α
      
    
    {\displaystyle \alpha }
  
 is most important. Stable count distributions have 
  
    
      
        0
        <
        α
        <
        1
      
    
    {\displaystyle 0<\alpha <1}
  
. The known analytical case of 
  
    
      
        α
        =
        1
        
          /
        
        2
      
    
    {\displaystyle \alpha =1/2}
  
 is related to the <a href="/facts/VIX/f3aKRvIR">VIX</a> distribution (See Section 7 of ). All the moments are finite for the distribution.
</p>

Stable count distribution open-in-new

Stable count distribution