Reading the evidence
A distribution shows which values occurred or are possible and how frequently or plausibly they appear. Shape reveals spread, skew, clusters and tails hidden by one average.
Make it click
An average height sign cannot show whether a route is flat or alternates cliffs and valleys. The full landscape explains the experience around the centre.
Now put that into markets
Return distributions can be empirical histories or model assumptions. Histograms, density plots and quantiles reveal different features.
Bin choices affect histograms, and limited samples estimate tails poorly. Normal models are convenient but often miss skew and extreme events.
Show count, period, units and missing values. Inspect centre, spread, asymmetry, modes and tails before fitting a named model.
Historical distribution need not remain stable, and apparent shape can depend on sampling frequency. A smooth curve can overstate certainty.
Takeaway
