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Distribution Fitting

Find which probability distribution best fits your data — and see how well it fits

Distribution fitting answers the question: what type of random process generated my data? Is it normally distributed (bell curve)? Exponentially distributed (memory-less decay)? Uniform (equally likely outcomes)? Knowing the distribution unlocks powerful probability calculations — "what fraction of values exceed X?" or "what is the 95th percentile?"

This tool loads 60 height measurements drawn from a near-normal distribution. Click Link Data and the AI will fit three candidate distributions, overlay the best curve on the histogram, and report which distribution wins with its parameters (μ, σ for normal).

Paste your own numeric column CSV to fit a distribution to your data.

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FAQ

What is a normal distribution?
The normal distribution (bell curve) is the most common distribution in nature. It is fully described by two parameters: the mean μ (center) and standard deviation σ (width). Many natural measurements — heights, weights, test scores — are approximately normally distributed.
What is goodness of fit?
Goodness of fit measures how well a theoretical distribution matches the observed data. Common tests include the Kolmogorov-Smirnov (K-S) test and the chi-squared test. A lower K-S statistic (or higher p-value) means a better fit.
How do I use the fitted distribution for predictions?
Once you know the distribution and its parameters, you can answer probability questions. For a normal distribution with μ = 170 and σ = 8: "What fraction of people are taller than 180 cm?" = P(X > 180) = P(Z > (180−170)/8) = P(Z > 1.25) ≈ 10.6%.
What if none of the distributions fit well?
If the data is bimodal (two peaks), skewed, or bounded, none of the three basic distributions may fit. In that case, consider transforming the data (e.g. log transform for right-skewed data) or using a non-parametric approach. The AI will flag poor fits and suggest alternatives.

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