Table 6 A boundary detection algorithm for probability density functions

Input: Observations \(D_{s}\) (s = 1,…,n), rescaling function g(⋅), and fitting model h(⋅).

For k from 1 to \(\max(D_{1},\ldots,D_{n})\) do:

 Fit h(⋅) to the PDF \(h_{0}(\cdot)\) of \(\{D_{s}, s=1,\ldots,n|D_{s} \leq k\}\) by maximum-likelihood estimation;

 Do KS test for two data g(h(t)) and \(g( h_{0}(t))\), t = 1,…,k with the null hypothesis they coming from the same distribution;

 Break if the test rejects the null hypothesis at significance level 5%.

Output: The current k as the boundary point.