My latest paper Proofs of Monotonicity for Truncated Johnson Power-Series Quantile Functions, coauthored with Professor J. Eric Bickel, is now out as preprint on SSRN! This is a short and sweet paper in which I proved two open conjectures in the original Truncated Johnson Power-Series Quantile Functions paper. The original work presented a novel formulation of the Johnson Quantile function family based on truncations of their power-series. I use some results from real-analysis to show that, for odd truncation order, the truncated SB and SL Johnson power-series are indeed monotonic and are therefore valid quantile functions. This was a short and enjoyable project that allowed me to dig into some technical proofs – Check it out!

JPSE_Conj
Figure. The derivative of the truncated Johnson SL power-series function with $K$ terms. For odd $K$, the derivative appears to be strictly positive in $z$ for any $\delta > 0$. This (and an analog for the SB power series) is the phenomenon we set out to rigorously prove. Taken from Truncated Johnson Power-Series Quantile Functions (Bickel, 2026).