Parabolic fractal distribution

<h2 id="definition">Definition</h2>
<p>The <a href="/facts/Probability_mass_function/LhurokRt">probability mass function</a> is given, as a function of the rank <i>n</i>, by
</p>

f
        (
        n
        ;
        b
        ,
        c
        )
        ∝
        
          n
          
            −
            b
          
        
        exp
        ⁡
        (
        −
        c
        (
        log
        ⁡
        n
        
          )
          
            2
          
        
        )
        ,
      
    
    {\displaystyle f(n;b,c)\propto n^{-b}\exp(-c(\log n)^{2}),}

<p>where <i>b</i> and <i>c</i> are parameters of the distribution.
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Zipf%2527s_law/bspk1du8">Zipf's law</a></li></ul>

<ul><li>Laherrère J, Deheuvels P (1996) <a href="http://www.hubbertpeak.com/laherrere/fractal.htm">"Distributions de type 'fractal parabolique' dans la nature"</a> (French, with English summary: "Parabolic fractal" distributions in nature), (<a href="http://www.hubbertpeak.com/laherrere/fractal.htm">http://www.hubbertpeak.com/laherrere/fractal.htm</a>) <i><a href="/facts/Comptes_rendus_de_l%2527Acad%25C3%25A9mie_des_sciences/9yR9XTN5">Comptes rendus de l'Académie des sciences</a>, Série II a: Sciences de la Terre et des Planétes</i>, 322, (7), 535–541</li>
<li>Xie, S.; Yang, Y. G.; Bao, Z. Y.; Ke, X. Z.; Liu, X. L. (2009). "Mineral resource analysis by parabolic fractals". <i>Mining Science and Technology (China)</i>. 19: 91–96. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2FS1674-5264%2809%2960017-X">10.1016/S1674-5264(09)60017-X</a>.</li></ul>

Parabolic fractal distribution open-in-new

Parabolic fractal distribution