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THE FEUTEX TOOLKIT

Hoeffding Mean Deviation Bound

Bound sample-mean deviations for independent observations with known finite limits.

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02 Your result
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FormulaTwo Sided Bound = min(1,2*exp(-2*n*error**2/(b-a)**2)); One Sided Bound = exp(-2*n*error**2/(b-a)**2)
Sources and model references

Worked example

Inputs

Independent observations
100 count
Lower bound
0 value
Upper bound
1 value
Deviation threshold
0.1 value

Expected results

Two Sided Bound
0.2706705665 probability
One Sided Bound
0.1353352832 probability

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "n": 100,
  "a": 0,
  "b": 1,
  "error": 0.1
}

Accuracy and scope

Independent bounded observations with common bounds; no distributional normality assumption. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.