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In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

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Proving a sequence of integrals increases (iterated minimax distributions)

Use Jensen's inequality and induction on $n$. Let $\phi_c(z) = (1- (1 - z)^c)^c$ , so that $\phi_c(F_i) = F_{i+1}$. As you noted, $\phi = f \circ f$, where $f(z) = (1-z)^c$. $f$ is convex for $0 \le …
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