Hyperbolic Temporal Discounting k Estimator
HyperbolicV=A/(1+kD) single indifference k=(A/V−1)/D, actual positive delay; negativek retained, not full behavioral calibration. Actual independently qualified instrument/cohort/matching units; no diagnosis, causal outcome, validated personal prediction or universal clinical cutoff.
Description
A hyperbolic discount parameter can be solved from one reward indifference point.
A hyperbolic discount parameter can be solved from one reward indifference point.1
Reward units and the delay unit determine the parameter's interpretation. The calculation and input requirements are explained below.
When to use Hyperbolic Temporal Discounting k Estimator
Enter positive delayed reward, positive immediate indifference reward in matching units, and positive delay.
How to use Hyperbolic Temporal Discounting k Estimator and how it works
- Prepare the measurements or independently established model inputs described below, with matching units and observation scope.
- Enter the required fields and run Hyperbolic Temporal Discounting k Estimator.
- Read the result fields using the formula, output units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualDelayedReward | Actual Delayed Reward. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
| actualImmediateIndifferenceReward | Actual Immediate Indifference Reward. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
| actualDelay | Actual Delay. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
Enter positive delayed reward, positive immediate indifference reward in matching units, and positive delay. Return (delayed/immediate-1)/delay, in reciprocal delay units. Negative values are retained if immediate reward exceeds delayed reward.
k=(delayedReward/immediateReward-1)/delay Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Numeric result under the formula and output units explained above. | number |
{
"input": {
"actualDelayedReward": 2,
"actualImmediateIndifferenceReward": 1,
"actualDelay": 2
},
"output": {
"result": {
"value": 0.5
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Thurstone Case V Scale Value Calculator for a complementary operation: Thurstone Case V scaling converts pairwise preference probabilities to normal deviates.
Use Prospect Value Function Alpha/Beta Estimator for a complementary operation: A power-value model becomes a straight line after logarithmic transformation.
References
Similar or alternative tools
- Thurstone Case V Scale Value Calculator
Thurstone Case V scaling converts pairwise preference probabilities to normal deviates.
- Prospect Value Function Alpha/Beta Estimator
A power-value model becomes a straight line after logarithmic transformation.