> ## Documentation Index
> Fetch the complete documentation index at: https://docs.meerietechnology.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Skewed and percentage shapes

> Lognormal, normal, split normal, logit-normal and Brown–Johnson: distributions for a likely range.

Use these shapes when you gave a **likely range** (low, middle, high), where about 1 in 10 falls below the low value and 1 in 10 above the high value. Most business estimates are this kind.

## The shapes

| Shape | Looks like | Good for | Chosen automatically when |
| - | - | - | - |
| **Skewed to the right (lognormal)** | Never below zero, with a long tail of occasional big values | Costs, volumes, durations | The low value is above zero |
| **Symmetric (normal)** | Equal spread both sides; can go below zero | Changes or differences that can go either way | The low value is zero or below |
| **Uneven range (split normal)** | Different spread below and above the middle | Lopsided ranges, for example likely 10, low 8, high 20 | Recommended when one shape fits your three numbers poorly |
| **Percentage (logit-normal)** | Stays strictly between 0% and 100% | Rates, shares, adoption, conversion | The answer is a percentage |
| **Uneven percentage (split logit-normal)** | As above, for lopsided ranges | Lopsided percentage ranges | Recommended when the plain percentage shape fits poorly |
| **Straight-line tails (Brown–Johnson)** | Straight lines through your three values, tails reaching 2.5 times each half-range, cut at any stated limits | Matching the method in Brown's *Business Case Analysis with R* | Never; choose it yourself |

## Rules of thumb

1. Can the value be negative? If not (costs, counts, times), use the **right-skewed** shape.
2. Is it a percentage? Use a **percentage** shape so it cannot go below 0% or above 100%.
3. Is your range lopsided? Use an **uneven** shape rather than forcing a symmetric one.
4. Is it really a few distinct cases, such as a contract won or lost? Use "a few outcomes" rather than a smooth range.
5. Do not choose a shape because it gives a nicer answer. Every choice is recorded in the model version.

## Fit warnings

The app checks the fit and tells you when it is poor.

> [accordion] “Your low, middle and high values do not fit the available shapes exactly”
>
> Your range is lopsided. The app shows the range it would actually use and recommends the uneven-range shape, which matches all three numbers exactly.

> [accordion] “This shape puts about X% of draws below zero”
>
> You chose a symmetric shape for something that cannot be negative, such as a cost. Switch to the right-skewed shape, or set a lower limit of zero.

> [!NOTE]
>
> The shape matters most for estimates at the top of the sensitivity ranking. For estimates that barely move the answer, the automatic choice is almost always good enough.

**Next:** [Correlation](https://docs.meerietechnology.com/estimate/correlation.md)


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