We investigate 1D exoplanetary distributions using a novel analysis algorithm based on the continuous wavelet transform. The analysis pipeline includes an estimation of the wavelet transform of the probability density function (p.d.f.) without pre-binning, use of optimized wavelets, a rigorous significance testing of the patterns revealed in the p.d.f., and an optimized minimum-noise reconstruction of the p.d.f. via matching pursuit iterations.
In the distribution of orbital periods, P, our analysis revealed a narrow subfamily of exoplanets within the broad family of "warm Jupiters", or massive giants with P greater than or similar to 300 d, which are often deemed to be related with the iceline accumulation in a protoplanetary disk. We detected a p.d.f. pattern that represents an upturn followed by an overshooting peak spanning P similar to 300-600 d, right beyond the "period valley". It is separated from the other planets by p.d.f. concavities from both sides. It has at least 2-sigma significance.
In the distribution of planet radii, R, and using the California Kepler Survey sample properly cleaned, we confirm the hints of a bimodality with two peaks about R =1.3 R-circle plus and R = 2.4 R-circle plus, and the "evaporation valley" between them. However, we obtain just a modest significance for this pattern, 2-sigma only at the best. Besides, our follow-up application of the Hartigan and Hartigan dip test for unimodality returns 3 per cent false alarm probability (merely 2.2-sigma significance), contrary to 0.14 per cent (or 3.2-sigma), as claimed by Fulton et al. (2017).
