Table 3 Less demanding choice of \({\text{D}}_{\text{k},\text{n}}\)s

E-divergence (Matteson and James 2013)

\(D(X,Y;\alpha )={\int }_{{R}^{d}}|{\phi }_{X}(t)-{\phi }_{Y}(t){|}^{2}(\frac{2{\pi }^{d/2}\Gamma (1-\alpha /2)}{\alpha {2}^{\alpha }\Gamma ((d+\alpha )/2)}|t{|}^{d+\alpha }{)}^{-1}dt>C\)

Parametric (Chen and Gupta 2011)

\({L}_{k}=-2log\frac{{L}_{0}(\hat{\lambda })}{{L}_{1}(\hat{\lambda },\hat{{\lambda }^{{{\prime}}}})}<C\)  

Pettitt (Pettitt 1979)

\({K}_{T}=ma{x}_{1\le t\le T}|\sum_{i=1}^{t}\sum_{j=t+1}^{T}sgn({X}_{i}-{X}_{j})|>C\)

Buishand (Buishand 1982)

\(U=\frac{1}{n(n+1)}\sum_{k=1}^{n-1}(\frac{{S}_{k}}{{D}_{x}}{)}^{2}\), where \({S}_{k}=\sum_{i=1}^{k}({X}_{i}-\overline{X}),{D}_{x}=sd(X)\)