Ebbinghaus Forgetting Curve

Evaluate a caller-calibrated exponential forgetting approximation with a nonzero floor; elapsed times and tau share one unit, and this is not a universal Ebbinghaus law.

Description

An exponential forgetting curve can decline toward a nonzero floor.

An exponential forgetting curve can decline toward a nonzero floor. The time constant sets the scale of decay above that floor.

The tool returns predictedRetentionFractions (predicted retention fractions). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Ebbinghaus Forgetting Curve

Use Ebbinghaus Forgetting Curve when you already have elapsedTimes, initialRetentionFraction, asymptoticRetentionFraction, timeConstant and want predictedRetentionFractions. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Ebbinghaus Forgetting Curve and understand its results

Enter elapsedTimes, initialRetentionFraction, asymptoticRetentionFraction, timeConstant using the field table below. Match the units, ordering and data boundaries described in the calculation.
Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
Read predictedRetentionFractions. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.

Input field	Meaning	Value type and bounds	Requirement
elapsedTimes	Elapsed times	list of number	Required
initialRetentionFraction	Initial retention fraction	number	Required
asymptoticRetentionFraction	Asymptotic retention fraction	number	Required
timeConstant	Time constant	number	Required

Evaluate nonnegative supplied times using fractions with floor≤initial and a positive time constant in matching units.

retention(t) = floor+(initial−floor)×exp(−t/tau)

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "elapsedTimes": [
      0,
      1,
      2
    ],
    "initialRetentionFraction": 1,
    "asymptoticRetentionFraction": 0.2,
    "timeConstant": 1
  },
  "output": {
    "predictedRetentionFractions": [
      1,
      0.4943035529371539,
      0.3082682265892902
    ]
  }
}

Limitations and assumptions

The model parameters are supplied rather than fitted, and individual learning or retrieval processes are not inferred.

Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.

Alternative or Complementary methods

Cognitive Decline Slope: Fit longitudinal cognitive score change after caller-supplied visit-specific practice offsets; score direction and diagnostic interpretation are not assumed. Recovery Time Constant Depression: Fit log(1−recovered fraction) against recovery interval to estimate exponential recovery tau; this model assumes an asymptotic recovery fraction of one.

Methodological background: Exponential distribution and decay model.^[1]

References

Exponential distribution and decay model — NIST/SEMATECH

Similar or alternative tools

Cognitive Decline Slope
Fit longitudinal cognitive score change after caller-supplied visit-specific practice offsets; score direction and diagnostic interpretation are not assumed.
Recovery Time Constant Depression
Fit log(1−recovered fraction) against recovery interval to estimate exponential recovery tau; this model assumes an asymptotic recovery fraction of one.