Generalized Pareto distribution
In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions. 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 \,}
  
.