Truncation (statistics)

<p>In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, truncation results in values that are limited above or below, resulting in a truncated sample. A random variable 
  
    
      
        y
      
    
    {\displaystyle y}
  
 is said to be truncated from below if, for some threshold value 
  
    
      
        c
      
    
    {\displaystyle c}
  
, the exact value of 
  
    
      
        y
      
    
    {\displaystyle y}
  
 is known for all cases 
  
    
      
        y
        >
        c
      
    
    {\displaystyle y>c}
  
, but unknown for all cases 
  
    
      
        y
        ≤
        c
      
    
    {\displaystyle y\leq c}
  
. Similarly, truncation from above means the exact value of 
  
    
      
        y
      
    
    {\displaystyle y}
  
 is known in cases where 
  
    
      
        y
        <
        c
      
    
    {\displaystyle y<c}
  
, but unknown when 
  
    
      
        y
        ≥
        c
      
    
    {\displaystyle y\geq c}
  
.
</p><p>Truncation is similar to but distinct from the concept of <a href="/facts/Censoring_(statistics)/aa8HkK1a">statistical censoring</a>. A truncated sample can be thought of as being equivalent to an underlying sample with all values outside the bounds entirely omitted, with not even a count of those omitted being kept. With statistical censoring, a note would be recorded documenting which bound (upper or lower) had been exceeded and the value of that bound. With truncated sampling, no note is recorded.
</p>

Truncation (statistics) open-in-new

Truncation (statistics)