Quick check · Quantile shape
Level III · Optional · Open anytime
Advanced Distributional Diagnostics
An advanced distributional review lab for quantitative researchers. Diagnose changes in shape, sample composition, joint extremes, downside concentration, and multivariate geometry. The aim is a defensible account of observed evidence, with an explicit boundary between a descriptive diagnostic, a sampling claim, and a deployment decision.
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Distributional shape · Section 1 of 2
Quantile asymmetry without relying on third moments
Moment skewness weights large deviations cubically, so a few extreme observations can dominate a short financial sample. A complementary descriptive measure is Bowley quartile skewness: (Q3 + Q1 − 2×median)/(Q3 − Q1), provided the IQR is positive. It compares distances on either side of the median within the central half.
A positive value means the upper half of that central interval extends farther from the median than the lower half. A negative value indicates the reverse. It lies between −1 and 1 when Q1 ≤ median ≤ Q3 and the IQR is positive. It is unchanged by a positive affine rescaling, but is undefined when Q1 equals Q3.
This measure deliberately ignores most extreme-tail magnitude. Two strategies can have the same quartiles and opposite crash behavior. Report it alongside tail observations rather than calling it a replacement for tail-risk analysis. Also keep the quartile convention and sampling window consistent across model versions.
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Keep in mind: Use quantile shape to complement moment summaries and retain a separate view of the extremes.
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Quick check · Tail interpretation
Two samples have identical quartiles but different worst losses. What must a review conclude?
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