Probability Density Function
A probability density function is used when outcomes are not just yes or no, but can take many possible values. Instead of assigning probability to a single point, it shows how probability is spread across an interval. Areas under the curve represent likelihood, not individual points.
In prediction markets, PDFs appear in markets with ranges, continuous values, or numeric outcomes. Traders collectively assign more weight to some values and less to others. On platforms like Polymarket, Kalshi, Myriad, and Manifold, this behavior is reflected in prediction markets data as smoother distributions rather than discrete odds. The PDF captures the market’s full belief shape.
As new information arrives, the shape of the density can shift, narrow, or skew. These changes reveal how expectations evolve, not just which outcome is most likely.
Why It Matters
Probability density functions show the full structure of uncertainty. They make prediction markets data more informative by revealing how belief is distributed across possible outcomes.
How is a probability density function used in prediction markets?
It is used to represent beliefs in markets with continuous or ranged outcomes. Instead of focusing on a single probability, analysts infer a density from outcome prices or bins. This allows prediction markets data to capture nuance in expectations across a spectrum of values.
How is a probability density function different from an outcome distribution?
An outcome distribution assigns probabilities to discrete outcomes. A PDF describes probability over a continuous range. In prediction markets data, PDFs are more suitable for numeric forecasts like prices, percentages, or measurements.
What can analysts learn from the shape of a probability density function?
They can see where belief is concentrated, how uncertain the forecast is, and whether risks are asymmetric. A narrow peak signals confidence, while a wide or skewed shape signals uncertainty or tail risk. These insights deepen interpretation of prediction markets data.
Real-World Example
A Kalshi market forecasts the range of an economic indicator. Instead of one likely value, probabilities cluster around several nearby values. Analysts use these probabilities to infer a probability density function that shows where the market expects the indicator to land.v
Probability Density Function and FinFeedAPI
Working with probability density functions requires access to full outcome-level probabilities. FinFeed's Prediction Markets API provides structured prediction markets data so developers and analysts can construct PDFs, analyze belief shapes, and model continuous forecasts.