Fit distributions to data
Paste or upload a series: returns, prices, claim sizes, durations or counts. Every standard quant model that can describe it is fitted by maximum likelihood and ranked by AIC. Then check the fit where it matters most, in the tails, with Q–Q plots, tail quantiles and the probability calculator. Everything runs in your browser; the data never leaves the page.
Your data
Histogram and fitted densities
Model ranking
Lower AIC and BIC are better. The Akaike weight is the relative likelihood that each model is the best of those fitted.
| Show | Model | Fitted parameters | Log-lik | AIC | ΔAIC | Weight | BIC | KS D | KS p* |
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* The KS p-value assumes the parameters were known in advance. Because they are estimated from the same data, the true p-value is smaller (Lilliefors, 1967), so treat it as optimistic. Use it to reject a model, not to accept one. It is not reported for counts.
Probability calculator
Compare the fitted models with the data on the question you care about, such as the chance of a daily loss worse than 3%. The answer for the first model shown is shaded on the chart.
Points on the line mean the model matches the data at that quantile. Bends at the ends show tails the model gets wrong.
Points on the line mean the model matches the data at that quantile. Bends at the ends show tails the model gets wrong.
Tail quantiles
Where risk lives: the empirical percentiles of the data vs. each shown model. The 1% and 99% rows are the one-day 99% VaR levels when the data are returns.