Distribution Fitting App
July 10, 2026 · View on GitHub
The Distribution Fitting app takes a set of data values and finds the probability distribution that best describes them. You load data, the app fits many candidate distributions, scores them, and recommends the best one — ready to use as an input model in a simulation.
You will need: Java 21 and some numeric data (a column of values). This guide uses a generated sample so you need nothing extra. New here? Read Common UI & concepts.
What you'll be able to do
- Load a dataset (from a file, a database, or pasted values).
- Explore it (statistics, histogram, plots).
- Fit and rank candidate distributions, and read the recommended fit.
- Read goodness-of-fit results and overlay plots.
1. At a glance
You move through the tabs Data → Analysis → Fitting → Reports (with Bootstrap for resampling). Load data, click Fit, and read the ranked results.
| Use this app when… | Use a sibling app when… |
|---|---|
| You have data and need an input distribution for a model. | You have a model and want to run it → Single / Scenario |
| You want to know "which distribution fits this?" | You want to analyze simulation output → Results app |
2. Before you begin
You need data. The Data tab adds datasets from four sources: a delimited file (CSV / whitespace), a SQLite database table, pasted/inline values, or generated samples. This guide uses 200 generated samples named Service Times. Each dataset is marked Continuous or Discrete, which determines the candidate distributions.
3. A guided tour of the window
- Menu bar — File, Appearance, Help, plus an Analysis name field that titles the reports.
- Tabs — Data, Analysis, Fitting, Reports, Bootstrap.
- Status bar — a validation indicator ("✓ configuration valid"), the file name, and the working directory.
4. Tutorial — fit a distribution to service times
Step 1 — Load the data (Data tab)
On the Data tab, pick a source from the Add datasets from: dropdown. For this guide choose Generated (sample) to create the 200 Service Times points, then click Generate dataset. Confirm its name and that it's marked Continuous.
Step 2 — Explore it (Analysis tab)
Pick the dataset and view its Statistics, Histogram, observation plot, and ACF. This is your sanity check before fitting — is the data shaped like something a standard distribution could match?
Step 3 — Fit candidate distributions (Fitting tab)
The Fitting tab (shown in §1) lists each dataset with its kind, an auto-shift flag, and how many estimators (9 here) and scoring models (4) will be used. Use Edit estimators… / Edit scoring… to customize, then click ▶ Fit. A progress bar runs and the row's status becomes Done.
Reading the results
The app ranks every fitted distribution by a multi-criteria score (BIC, Anderson–Darling, Cramér–von Mises, and a Q-Q correlation). Below is the genuine ranking for our data — the same output the Reports tab produces:
| Distribution (best first) | BIC | AD | CVM | Avg Rank | |
|---|---|---|---|---|---|
| Weibull (shape 1.28, scale 11.82) | 1 | 1 | 1 | 1 | 1.00 |
| Gamma (shape 1.35, scale 8.19) | 2 | 3 | 3 | 2 | 2.50 |
| GeneralizedBeta | 4 | 2 | 2 | 3 | 2.75 |
| Exponential (mean 11.04) | 3 | 5 | 5 | 4 | 4.25 |
| Normal | 6 | 4 | 4 | 6 | 5.00 |
The recommended distribution is a shifted Weibull(shape ≈ 1.28, scale ≈ 11.82) (overall score 0.97). The density overlay shows the fitted curve against the data histogram — a close match:
How to read it. Weibull ranks first on all four criteria, so it's the clear recommendation here. (The data was in fact generated from a Gamma distribution, which ranks a close second — with only 200 points, Weibull and Gamma are nearly indistinguishable, a useful reminder that "best fit" is a statistical judgment, not a certainty.) The app also produces Q-Q, P-P, and ECDF plots and formal goodness-of-fit tests to confirm the choice.
5. Reference — every tab explained
| Tab | What it's for |
|---|---|
| Data | Import datasets (file / database / inline); set each as Continuous or Discrete. |
| Analysis | Exploratory analysis of one dataset: statistics, histogram, observation/ACF plots, shift analysis, and a one-click full analysis report. |
| Fitting | Configure estimators, scoring, and per-parameter bootstrap per dataset; run the fit; see per-dataset status. |
| Reports | Open the recommended distribution or all fitted distributions report (HTML). |
| Bootstrap | Resample to assess how stable the recommended-family choice is. |
6. Common tasks
| Task | How |
|---|---|
| Fit several datasets at once | Add them all on Data; tick incl; Fit runs the batch |
| Restrict the candidate distributions | Edit estimators… on the Fitting tab |
| Force/disable an automatic shift | The shift checkbox / Auto-shift: all / none |
| See how confident the family choice is | Run the Bootstrap tab |
| Open the recommended-fit report | Reports tab → Recommended distribution → Open in browser |
7. Troubleshooting & gotchas
| Symptom | Cause | Fix |
|---|---|---|
| A discrete-only distribution won't fit | The dataset is marked Continuous (or vice-versa). | Set the correct kind on the Data/Fitting tab. |
| The recommended fit looks poor | The data may need a shift, or no standard family fits well. | Enable auto-shift; inspect the Q-Q/P-P plots; consider an empirical distribution. |
| Fit produces no results | No datasets included, or none selected. | Tick incl for at least one dataset. |
| Top two distributions are nearly tied | Small sample; similar families. | Collect more data, or use the Bootstrap tab to judge stability. |
8. See also
- Common UI & concepts · Single-Model app — uses the fitted distribution as a model input.
- KSL Book — input modeling and distribution fitting.