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Timeline for Reshaping a Gamma random variable?

Current License: CC BY-SA 4.0

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May 19, 2020 at 15:11 comment added lrnv Thanks about the comment regarding the complexity. However I do have more analytical need than computational : E.g, computing the c.g.f $K(t,s) = log\left(\mathbb{E}\left(e^{-tX - sf(X)}\right)\right)$ for later inversion purposes. Hence my goal to obtain a 'usable' form for $f$.
May 19, 2020 at 14:40 comment added Iosif Pinelis @lrnv : I have added a comment concerning the complexity of the expression $F_2^{-1}\circ F_1$.
May 19, 2020 at 14:38 history edited Iosif Pinelis CC BY-SA 4.0
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May 19, 2020 at 13:40 vote accept lrnv
May 19, 2020 at 13:39 comment added lrnv Yes, i do need it to be monotonic. Thanks for the proof it's stunning now. The problem now becomes 'Is there a nice expression of $F_2^{-1} \circ F_1$' which i'm afraid has to be ansewred by a strict No... Too bad.
May 19, 2020 at 12:48 history edited Iosif Pinelis CC BY-SA 4.0
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May 19, 2020 at 12:43 history answered Iosif Pinelis CC BY-SA 4.0