Examples
Examples
Try the starting example
- Items: name, minimum $, mode $, maximum $, quantile group or independent
- Design,100,150,200,independent Build,300,400,500,independent
- Simulation trials: 20–10000
- 2000
- Unsigned 32-bit seed
- 42
- Budget threshold ($)
- 600
- Simulated mean total cost ($)
- $551.00
- Empirical median cost ($)
- $550.99
- Empirical 90th-percentile cost ($)
- $610.08
- Trials at or below budget (%)
- 86.25
- Monte Carlo standard error of mean ($)
- $1.00
- Absolute difference between half-run means ($)
- $0.97
Try another scenario
- Items: name, minimum $, mode $, maximum $, quantile group or independent
- Design,100,150,200,market Build,300,400,500,market
- Simulation trials: 20–10000
- 2000
- Unsigned 32-bit seed
- 42
- Budget threshold ($)
- 600
- Simulated mean total cost ($)
- $552.16
- Empirical median cost ($)
- $551.73
- Empirical 90th-percentile cost ($)
- $633.11
- Trials at or below budget (%)
- 77.85
- Monte Carlo standard error of mean ($)
- $1.36
- Absolute difference between half-run means ($)
- $1.57
Calculation method
Calculation method
Simulated mean total cost ($)
Draw triangular costs and sum items per trial. Shared named groups reuse one uniform quantile within a trial; independent rows use separate draws.
Empirical median cost ($)
Nearest-rank empirical 50th percentile.
Empirical 90th-percentile cost ($)
Nearest-rank empirical 90th percentile.
Trials at or below budget (%)
Fraction of totals ≤ the supplied budget, multiplied by 100.
Monte Carlo standard error of mean ($)
Sample standard deviation with n−1 denominator, divided by sqrt(trials).
Absolute difference between half-run means ($)
Compare first-half and second-half sample means as a simple convergence diagnostic.
Symbols and units
- a
- Items: name, minimum $, mode $, maximum $, quantile group or independent
- b
- Simulation trials: 20–10000
- c
- Unsigned 32-bit seed
- d
- Budget threshold ($)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- A reproducible triangular-input simulation using an unsigned 32-bit LCG and open-interval uniform quantiles. Named groups represent perfect positive quantile dependence; arbitrary correlations are not inferred. Model uncertainty is separate from Monte Carlo sampling error. Up to 40 items and 10,000 trials.
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Further reading
NIST: triangular-input Monte Carlo example ↗
Background reading; this does not imply endorsement or independent review of SumFizz.