limitAsProbabilityApproachesZero

The limit of the quantile function in fitting space as the cumulative probability approaches zero.

A metalog whose declared bounds are infinite is not necessarily unbounded. Keelin notes that the quantile function is bounded whenever every coefficient carrying the logit is zero, the four-term uniform being the familiar example. In that case the logit weight vanishes and the limit is finite, because the logit diverges only logarithmically while its weight approaches zero linearly. Otherwise the limit is negative infinity.

The test for a vanishing weight is exact, so a fitted metalog whose weight is merely small is correctly reported as diverging.