Playground for testing Quantile Mapping
Module : QuantileMapping.ParametricQM
Apply exact formula F^1_data F_simul(x)
correction.ppf(simulation.cdf(input))
When the ppf and cdf are known this is exact
Module : QuantileMapping.QMqqMap
Create a quantile - quantile map, including uncertainties
Module : QuantileMapping.QuantileHelper
Implement approximate non parametric confidence intervals for quantiles.
Following "Confidence interval for quantiles and percentiles",
Cristiano Ialongo
doi: 10.11613/BM.2019.010101
Introduce distortion to a normal distibution.
Derive a correction by fitting the quantile-quantile plot
Compare it with the known exact Quantile Map correction
Compare it with the Shift and Stretch.