Loading page
About this tool
Fit your dataset against common probability distributions and compare goodness of fit.
The Probability Distribution Fitter takes a numeric sample, estimates the parameters of the normal, exponential and lognormal distributions from it, and ranks those candidates by AIC = 2k − 2·lnL so you can see which shape describes your data best. Parameters come from the sample moments: the normal gets the sample mean and the population standard deviation, the exponential gets λ = 1/mean, and the lognormal gets the mean and standard deviation of the logged values. It is a quick exploratory comparison for students and analysts deciding which model is worth pursuing, not a goodness-of-fit test.
Open Probability Distribution Fitter on AltFTool — it loads instantly in your browser.
Enter the values you already know.
Fine-tune the options to match your scenario.
Read the result and use it in your planning or reporting.
All three candidates are scored on the same sample so you compare AIC values side by side instead of eyeballing a single curve.
AIC charges 2 per parameter, so the one-parameter exponential is not beaten by the two-parameter lognormal on log-likelihood alone.
Exponential and lognormal are only offered when every value in the sample is strictly positive, since both are undefined at or below zero.
AIC = 2k − 2·lnL, where k is the number of estimated parameters: 2 for the normal (mean and standard deviation), 1 for the exponential (λ), and 2 for the lognormal (μ and σ of the logs). Lower is better, and the lowest-scoring model is reported first.
Because at least one value in the sample is zero or negative, or the positive-only toggle is off. Both distributions have support only on the positive reals, so their log-likelihoods are undefined for non-positive data and the comparison is limited to the normal.
No. AIC ranks the candidates against each other, so the winner is only the best of the two or three models tried — it can still fit badly. Confirm with an actual goodness-of-fit test such as Kolmogorov-Smirnov or Anderson-Darling, plus a Q-Q plot, before relying on the choice.
At least 2 for the tool to return anything, but that is a floor for the arithmetic, not a sensible sample. AIC comparisons between two-parameter models are unstable on small samples; a few dozen observations is a more realistic minimum, and tail behaviour needs considerably more.
Add the Probability Distribution Fitter widget to your blog or website — free, responsive, no signup. Just keep the “Widget by AltFTool” credit link visible.
<iframe src="https://www.altftool.com/embed/widget/probability-distribution-fitter"
title="Probability Distribution Fitter — free AltFTool widget"
width="100%" height="640" style="border:0;border-radius:12px;overflow:hidden"
loading="lazy" referrerpolicy="no-referrer-when-downgrade" allow="clipboard-write"></iframe>
<p style="font-size:12px;margin:4px 0 0">Widget by <a href="https://www.altftool.com/tools/all/probability-distribution-fitter?utm_source=embed&utm_medium=widget" rel="nofollow">AltFTool — free online tools</a></p>