Inverse of KT Probability Weighting Function http://oi67.tinypic.com/28uo45i.jpg I'm trying to find the inverse function of above. I can't seem to get it right, and websites such as wolfram and symbolab aren't working for me as well. Would be great to get some pointers. Many thanks! (Relates to my thesis) 
That would involve solving a 'polynomial' of degree . (I put "polynomial" in quotes because is not necessarily an integer. There is no general formula for that. 
$\omega = \left(\dfrac{p^\gamma}{p^\gamma+(1p)^\gamma}\right)^\frac 1 \gamma$ $\omega^\gamma = \dfrac{p^\gamma}{p^\gamma+(1p)^\gamma}$ $\omega^\gamma = \dfrac{1}{1+\left(\frac{1p}{p}\right)^\gamma}$ $\omega^{\gamma} = 1+\left(\frac{1p}{p}\right)^\gamma$ $\omega^{\gamma}1 = \left(\frac{1p}{p}\right)^\gamma$ $\left(\omega^{\gamma}1 \right)^{\frac 1 \gamma} = \dfrac{1p}{p} = \dfrac 1 p  1$ $\left(\omega^{\gamma}1 \right)^{\frac 1 \gamma} +1 = \dfrac 1 p$ $p = \dfrac{1}{\left(\omega^{\gamma}1 \right)^{\frac 1 \gamma} +1 }$ 
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But, thanks nonetheless, I think I have an idea now 
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Nevermind, I seem to have confused myself again. Your help would be greatly appreciated! 
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You'll have to use numeric methods. 
Toying with this a bit in Mathematica produced $p \approx 0.477328 0.502426 \cos (3.33061 \omega+0.141105), ~\omega \in [0,1]$ as a pretty good fit to an inverse of the curve with $\gamma = 0.65$ 
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I tried graphing that alongside the original equation, but the results were a bit weird. I'm trying to go for something like this: http://oi63.tinypic.com/2zgsydj.jpg Where the green line is the inverse, and the red line is the original. Is this worth pursuing? 
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