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Non Linear ODE whose solution is can be viewed as a cumulative distribution function

  1. Jan 10, 2012 #1
    Let X be continuous a random variable who's support is the entire real line and who's cumulative distribution function satisfies the initial value problem

    F'(x)=s[itex]\cdot[/itex]F(x)a[itex]\cdot[/itex](1-F(x))b
    F(m)=1/2

    note that a>0, b>0, s>0 and m is real. m is the median of the distribution,


    Is it possible to explicitly solve for the CDF, F(x), the PDF f(x)=F'(x), the moment or probability generating functions for X, and/or the inverse function of the CDF
     
  2. jcsd
  3. Jan 10, 2012 #2
    Re: Non Linear ODE whose solution is can be viewed as a cumulative distribution funct

    It is possible to solve the ODE. The result is x as a function of F thanks to the Incomplete Beta Function. Then F(x) is the inverse function.
     
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