Convergance by Testing Percentiles

Background

Percentiles can require very different numbers of iterations to converge and may converge faster or slower than the mean, even though the mean is generally more stable.

This is because @RISK’s convergence test evaluates whether a percentile estimate is within a percentage tolerance of the true percentile with a specified confidence.

Details

Convergence tolerance is proportional to the percentile’s value.

• Small percentile values (e.g., P1 near zero) produce extremely small tolerances and therefore require many more iterations.
• Large percentile values (e.g., P99 in a wide distribution) produce larger tolerances and converge quickly. If values are negative, the relationship reverses.
• Distributions with very narrow ranges can appear to “converge” instantly because the tolerance band is wider than the data range.

P50 often converges more slowly than extreme percentiles because binomial-based uncertainty is largest near 50%.

• Means often converge faster than P50 because the mean uses Student’s t, which typically yields tighter confidence intervals than the binomial.

Guidance:

Run a small preliminary simulation to gauge scale.

If the percentile of interest is near zero, increase tolerance or use a different statistic. Ensure the tolerance is appropriate relative to the variable’s range; adjust upward or downward as needed.

 

Related Articles:

Convergence Monitoring in @RISK

 Distribution-Free Confidence Intervals for Percentiles