Dyadic distribution

<h2 id="definition">Definition</h2>
<p>A dyadic distribution is a <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a> whose <a href="/facts/Probability_mass_function/LhurokRt">probability mass function</a> is
</p>

f
        (
        i
        )
        =
        
          2
          
            −
            
              x
              
                i
              
            
          
        
      
    
    {\displaystyle f(i)=2^{-x_{i}}}

<p>where 
  
    
      
        
          x
          
            i
          
        
      
    
    {\displaystyle x_{i}}
  
 is some whole number.
</p><p>It is possible to find a binary code defined on this distribution, which has an average code length that is equal to the <a href="/facts/Entropy/s52IXeFz">entropy</a>.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a>
</p>

<ul><li>Cover, T.M., Joy A. Thomas, J.A. (2006) <i>Elements of information theory</i>, Wiley. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-471-24195-4</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Cover, T.M., Joy A. Thomas, J.A. (2006) Elements of information theory, Wiley. ISBN 0-471-24195-4
 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Dyadic distribution open-in-new

Dyadic distribution