Example stratification of probability space into 20 bins using three distribution transformations: Uniform, Normal, and Extreme Value Type I (EV1/Gumbel). Demonstrates how different transformations allocate sampling effort across the probability range, with EV1 concentrating more bins in the rare event tail critical for dam safety analysis.
Format
A data frame with 60 rows and 5 columns:
- distribution
Stratification distribution type: "uniform", "normal", or "ev1"
- bin
Bin number (1-20), ordered from most frequent to most rare events
- lower
Lower bound of the bin in the distribution's transformed space (probability for Uniform, z-score for Normal, Gumbel reduced variate for EV1)
- upper
Upper bound of the bin in the distribution's transformed space
- weight
Probability weight of the bin, representing the fraction of the total probability captured by each bin. Weights sum to approximately 1 within each distribution.
Examples
example_stratified[sample(nrow(example_stratified), 5), ]
#> distribution bin lower upper weight
#> 33 normal 13 2.43666160 2.83357905 0.005110276
#> 5 uniform 5 0.79200000 0.74250000 0.049499999
#> 10 uniform 10 0.54450000 0.49500001 0.049500000
#> 20 uniform 20 0.04950001 0.00000001 0.049500010
#> 16 uniform 16 0.24750001 0.19800001 0.049500000