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Builds a three-term metalog from a symmetric percentile triplet, using the closed form of Keelin (2016) Proposition 1 and its bounded counterparts in Propositions 3 and 4.
The three quantiles correspond to cumulative probabilities of alpha, one half, and one minus alpha. Supplying a finite bound selects the semi-bounded or bounded member, in which case each quantile must lie strictly inside the bounds.
Not every triplet describes a valid distribution. A median too close to either outer quantile demands more skewness than three terms can express, and this function fails in that case. Test a triplet first with the companion predicate, or add terms.
Parameters
the quantile at cumulative probability alpha
the quantile at cumulative probability one half
the quantile at cumulative probability one minus alpha
the probability offset, which must lie strictly within zero and one half
the lower bound, or negative infinity when unbounded below
the upper bound, or positive infinity when unbounded above
an optional name