Bass Diffusion p, q Adoption Calculator
Conditional continuous Bass cumulative-adoption model with independently calibrated p>0, q≥0, time≥0, no initial adoption. Not a prediction without calibration, market-size constraint or causal peer-effect estimate.
Description
The Bass model represents adoption using calibrated innovation and imitation terms.
The Bass model represents adoption using calibrated innovation and imitation terms.1
Its closed-form cumulative fraction depends on an adopted market and time convention rather than automatically fitted sales history.
When to use Bass Diffusion p, q Adoption Calculator
Use this tool to obtain conditionalCumulativeAdoptionFraction from the supplied records using the stated calculation. Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
How to use Bass Diffusion p, q Adoption Calculator and understand its results
- Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
- Enter callerCalibratedInnovationP, callerCalibratedImitationQ, timeYears, using the field meanings and rules below, then run the tool.
- Read result.conditionalCumulativeAdoptionFraction. Use the units and sign conventions below, and review any unknown records separately.
- Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| callerCalibratedInnovationP | Caller calibrated innovation p | number | Required |
| callerCalibratedImitationQ | Caller calibrated imitation q | number | Required |
| timeYears | Time years | number | Required |
Require positive innovation p, nonnegative imitation q and nonnegative elapsed years on their compatible inverse-year basis. Evaluate the closed-form cumulative Bass fraction; time zero returns zero. Parameters are supplied, not fitted; no market-size multiplication or adoption-flow derivative is returned.
F(t)=(1−exp(−(p+q)t))/(1+(q/p)×exp(−(p+q)t)) Use the matching field units and the exact boundary, ordering and reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Calculated observation or qualified reference | object |
| result.conditionalCumulativeAdoptionFraction | Cumulative Bass model fraction at supplied time with supplied innovation/imitation parameters. | number |
{
"input": {
"callerCalibratedInnovationP": 0.03,
"callerCalibratedImitationQ": 0.38,
"timeYears": 0
},
"output": {
"result": {
"conditionalCumulativeAdoptionFraction": 0
}
}
}Limitations and assumptions
Population definitions, survey design, calibration and observation coverage are independently established. A result describes the supplied record or conditional model without demonstrating causation, validating an instrument or supplying representative population evidence.
Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related step, use Granovetter Threshold Distribution Checker: A participation-threshold model updates people according to a declared active-population count. For a complementary comparison, use Six-Degrees Hop Small-World Estimator: A tree-like small-world approximation relates population size to effective branching degree.
References
-
Bass Diffusion p, q Adoption Calculator — tool.io
Similar or alternative tools
- Granovetter Threshold Distribution Checker
A participation-threshold model updates people according to a declared active-population count.
- Six-Degrees Hop Small-World Estimator
A tree-like small-world approximation relates population size to effective branching degree.