Generalized Pareto distribution

<p>In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, the generalized Pareto distribution (GPD) is a family of continuous <a href="/facts/Probability_distribution/EpsKKVRu">probability distributions</a>. It is often used to model the tails of another distribution. It is specified by three parameters: location 
  
    
      
        μ
      
    
    {\displaystyle \mu }
  
, scale 
  
    
      
        σ
      
    
    {\displaystyle \sigma }
  
, and shape 
  
    
      
        ξ
      
    
    {\displaystyle \xi }
  
. Sometimes it is specified by only scale and shape and sometimes only by its shape parameter. Some references give the shape parameter as 
  
    
      
        κ
        =
        −
        ξ
        
      
    
    {\displaystyle \kappa =-\xi \,}
  
.
</p><p>With shape 
  
    
      
        ξ
        >
        0
      
    
    {\displaystyle \xi >0}
  
 and location 
  
    
      
        μ
        =
        σ
        
          /
        
        ξ
      
    
    {\displaystyle \mu =\sigma /\xi }
  
, the GPD is equivalent to the <a href="/facts/Pareto_distribution/PgMDbLrR">Pareto distribution</a> with scale 
  
    
      
        
          x
          
            m
          
        
        =
        σ
        
          /
        
        ξ
      
    
    {\displaystyle x_{m}=\sigma /\xi }
  
 and shape 
  
    
      
        α
        =
        1
        
          /
        
        ξ
      
    
    {\displaystyle \alpha =1/\xi }
  
.
</p>

Generalized Pareto distribution open-in-new

Generalized Pareto distribution