Parametric Bootstrap Confidence Interval Estimation for the Percentile and Difference between the Percentiles of Delta-Lognormal Distributions with Application to Rainfall Data in Thailand

In Thailand, flooding often occurs during the summer monsoon when many tropical storms affect the country. The motivation of this study was to plan for and mitigate the damage caused by flooding in the future. The confidence interval (CI) for the percentile of a precipitation dataset can be used to estimate the intensity of rainfall in a particular area whereas the CI for the difference between the percentiles of two datasets can be used to compare the rainfall intensities in two areas. To this end, the performances of several approaches to estimate the CI for the percentile and difference between the percentiles of delta -lognormal distributions were constructed and compared. These estimates were constructed based on the Bayesian (BS) and parametric bootstrap (PB) approaches, as well as two fiducial generalized confidence interval (FGCI) approaches. The performances of the methods were evaluated using Monte Carlo simulation, the results of which indicate that the PB approach for both CIs performed the best in all scenarios tested. Its suitability was confirmed via two illustrative examples using daily rainfall datasets for Chiang Mai and Lampang provinces in Thailand.