You guessed min, likely, max. What does history say?
Every simulation input is a claim about shape. Distribution Fitting tests that claim against your actual history, ranks the candidates, and hands back exact parameters instead of three guesses.
Analytics Starter Statistics free
After you install, this is the model to open.
Which Distribution Fits Your Data?
- In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
- Click Start from a template and put that name in the search box.
- Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.
The answer
The skew decides it, exactly as it should:
- Lognormal
- KS 0.086 winner
- Triangular
- KS 0.119
- Normal
- KS 0.158 last
A bell curve loses because it is symmetric and delivery times are not: no parcel arrives four days early to balance the one that came four days late. The payoff line reads Lognormal(mean 5.2402, sd 2.6855), parameters you can type straight into a Risk Analysis input. Fit lead times, repair durations, or claim sizes; eight values is the floor. The winning fit also saves as a SIPmath 3.0 library, the open standard from probabilitymanagement.org, ready for any tool that reads one.
The model
Sixteen supplier deliveries: most arrive in three to five days, the tail stretches to 12.3. Each candidate distribution is fitted and scored by the Kolmogorov-Smirnov statistic, smaller is closer, and the report carries a chi-square check, approximate p-values and the AIC and BIC picks beside that ranking, so the winner can be argued with.
| Delivery times | 16 orders, 2.1 to 12.3 days |
| Candidates | normal, lognormal, triangular, uniform |
| KS ranking | calculated |
| Best-fit parameters | calculated |
Once it is in your sheet
- The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
- Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
- Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.
Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.
Next question
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- How do you know a forecast method actually works?Make a Demand Series to Test a Model
- Do ads move your sales, or is it price?What Actually Drives Your Sales?
Every model like this one, and the method behind them: Statistics in Google Sheets.