Estimates cumulative distribution functions and quantiles under local differential privacy. Provides binary and categorical randomization mechanisms, isotonic distribution estimators, and simulation interfaces for sequential quantile estimation with self-normalized inference and asymptotic confidence sequences. Distribution estimators operate on privatized reports; quantile interfaces simulate local randomization internally. Methods include the quantile procedure of Liu et al. (2023) < https://proceedings.mlr.press/v202/liu23q.html> and the distribution estimator of Liu, Hu and Kong (2024) < https://proceedings.mlr.press/v235/liu24z.html>.