Full Distribution#
Predicting the entire outcome distribution rather than a single value.
Important
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What it is#
Forecasting the full distribution means predicting the entire predictive distribution — the complete CDF / PDF over all possible outcomes — rather than a summary of it. A point forecast collapses it to one number; a quantile forecast reports a few points; the full distribution keeps everything.
The richest target#
From the full distribution you can derive any summary after the fact — the mean, the median, any quantile, a prediction interval, the probability of exceeding a threshold, or a risk measure such as VaR. Nothing about the uncertainty is discarded.
How it’s judged#
Because it is a whole distribution, it is scored by a rule that reads the entire shape against the outcome — the CRPS, which compares the forecast CDF to the observation’s step CDF — not a point-error metric like MAE.
Theme: Risk & Probabilistic Forecasting · All terminology
Hint
Mind map — connected ideas
Continuous Probabilistic Forecasts · Probabilistic Forecasts · Point Forecasts · Quantile Forecasts · Probability Distribution · Probabilistic Scoring
Hint
More in Risk & Probabilistic Forecasting
Continuous Probabilistic Forecasts · Continuous Ranked Probability Score (CRPS) · Deterministic forecasts · Pinball Loss (a.k.a. Quantile Loss) · Point Forecasts · Predicting Percentiles · Prediction Intervals (PI) · Probabilistic Forecasts · Probabilistic Scoring · Probability Forecasts · Quantile Forecasts · Quantile Level · Quantile Regression · Return Distribution
See also
Source article Adapted (context, re-expressed) in our own words from: Full Distribution (insightful-data-lab.com).