Calculator
Inputs and options
Example data table
This sample illustrates a unimodal distribution. Paste these values into the calculator to see a smooth estimate.
| # | Value |
|---|---|
| 1 | 1.2 |
| 2 | 1.9 |
| 3 | 2.1 |
| 4 | 2.6 |
| 5 | 2.9 |
| 6 | 3 |
| 7 | 3.4 |
| 8 | 3.8 |
| 9 | 4.2 |
| 10 | 4.6 |
| 11 | 4.9 |
| 12 | 5.1 |
Formula used
For data points x₁, x₂, …, xₙ, the kernel density estimate at x is:
f̂(x) = (1 / (n·h)) · Σ K( (x − xᵢ) / h )
- K(·) is the selected kernel function.
- h is bandwidth; it controls smoothness.
- Rule-of-thumb bandwidths scale with n^(−1/5).
How to use this calculator
- Paste your numeric sample into Sample data.
- Select a Kernel and choose a Bandwidth method.
- Pick Auto grid or provide Custom x values.
- Click Estimate Density to show results above the form.
- Use Download CSV or Download PDF for sharing.