Techniques used to smooth the nearest values when calculating quantile functions. R2 is used by default, and the numbering convention follows the use in the R programming language, as far as it goes.
Inverse of the empirical distribution function
.. with averaging at discontinuities (default)
The observation numbered closest to Np. NB: does not yield a proper median
Linear interpolation of the empirical distribution function. NB: does not yield a proper median.
.. with knots midway through the steps as used in hydrology. This is the simplest continuous estimator that yields a correct median
Linear interpolation of the expectations of the order statistics for the uniform distribution on [0,1]
Linear interpolation of the modes for the order statistics for the uniform distribution on [0,1]
Linear interpolation of the approximate medans for order statistics.
The resulting quantile estimates are approximately unbiased for the expected order statistics if x is normally distributed.
When rounding h, this yields the order statistic with the least expected square deviation relative to p.
The Harrell-Davis quantile estimator based on bootstrapped order statistics