SumErf:	${\displaystyle \sum _{L=1}^N\text{erf}}\frac{\frac{x_L}{{\mathbf{\sigma }}^2}}{\sqrt{2\left(\frac{1}{{\mathbf{\sigma }}^2}+\frac{1}{{\mathbf{\sigma }}_{\mathrm{s}}^2}\right)}}>0$
SumErfT1:	${\displaystyle \sum _{L=1}^N\text{erf}}\frac{\frac{x_L}{{\mathbf{\sigma }}^2}}{\sqrt{2\left(\frac{1}{{\mathbf{\sigma }}^2}+\frac{1}{{\mathbf{\sigma }}_{\mathrm{s}}^2}\right)}}\exp \left(-\frac{x_L^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+{\mathbf{\sigma }}^2\right)}\right)>0,$
SumErfT2:	${\displaystyle \sum _{L=1}^N\text{erf}}\frac{\frac{x_L}{{\mathbf{\sigma }}^2}}{\sqrt{2\left(\frac{1}{{\mathbf{\sigma }}^2}+\frac{1}{{\mathbf{\sigma }}_{\mathrm{s}}^2}\right)}}\exp \left(-\frac{{\overline{\mathbf{x}}}_{\backslash L}^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+\frac{{\mathbf{\sigma }}^2}{N-1}\right)}\right)>0,$
SumErfT3:	${\displaystyle \sum _{L=1}^N\text{erf}}\frac{\frac{x_L}{{\mathbf{\sigma }}^2}}{\sqrt{2\left(\frac{1}{{\mathbf{\sigma }}^2}+\frac{1}{{\mathbf{\sigma }}_{\mathrm{s}}^2}\right)}}\exp \left(-\frac{N-1}{2{\mathbf{\sigma }}^2}\mathrm{var}{\mathbf{x}}_{\backslash L}\right)>0,$
SumErfT12:	${\displaystyle \sum _{L=1}^N\text{erf}}\frac{\frac{x_L}{{\mathbf{\sigma }}^2}}{\sqrt{2\left(\frac{1}{{\mathbf{\sigma }}^2}+\frac{1}{{\mathbf{\sigma }}_{\mathrm{s}}^2}\right)}}\exp \left(-\frac{x_L^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+{\mathbf{\sigma }}^2\right)}-\frac{{\overline{\mathbf{x}}}_{\backslash L}^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+\frac{{\mathbf{\sigma }}^2}{N-1}\right)}\right)>0,$
SumErfT13:	${\displaystyle \sum _{L=1}^N\text{erf}}\frac{\frac{x_L}{{\mathbf{\sigma }}^2}}{\sqrt{2\left(\frac{1}{{\mathbf{\sigma }}^2}+\frac{1}{{\mathbf{\sigma }}_{\mathrm{s}}^2}\right)}}\exp \left(-\frac{x_L^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+{\mathbf{\sigma }}^2\right)}-\frac{N-1}{2{\mathbf{\sigma }}^2}\mathrm{var}{\mathbf{x}}_{\backslash L}\right)>0,$
SumErfT23:	${\displaystyle \sum _{L=1}^N\text{erf}}\frac{\frac{x_L}{{\mathbf{\sigma }}^2}}{\sqrt{2\left(\frac{1}{{\mathbf{\sigma }}^2}+\frac{1}{{\mathbf{\sigma }}_{\mathrm{s}}^2}\right)}}\exp \left(-\frac{{\overline{\mathbf{x}}}_{\backslash L}^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+\frac{{\mathbf{\sigma }}^2}{N-1}\right)}-\frac{N-1}{2{\mathbf{\sigma }}^2}\mathrm{var}{\mathbf{x}}_{\backslash L}\right)>0,$
SumXT1:	${\displaystyle \sum _{L=1}^N{x}_L\exp \left(-\frac{x_L^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+{\mathbf{\sigma }}^2\right)}\right)>0,}$
SumXT2:	${\displaystyle \sum _{L=1}^N{x}_L\exp \left(-\frac{{\overline{\mathbf{x}}}_{\backslash L}^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+\frac{{\mathbf{\sigma }}^2}{N-1}\right)}\right)>0,}$
SumXT3:	${\displaystyle \sum _{L=1}^N{x}_L\exp \left(-\frac{N-1}{2{\mathbf{\sigma }}^2}\mathrm{var}{\mathbf{x}}_{\backslash L}\right)>0,}$
SumXT12:	${\displaystyle \sum _{L=1}^N{x}_L\exp \left(-\frac{x_L^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+{\mathbf{\sigma }}^2\right)}-\frac{{\overline{\mathbf{x}}}_{\backslash L}^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+\frac{{\mathbf{\sigma }}^2}{N-1}\right)}\right)>0,}$
SumXT13:	${\displaystyle \sum _{L=1}^N{x}_L\exp \left(-\frac{{\overline{\mathbf{x}}}_{\backslash L}^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+\frac{{\mathbf{\sigma }}^2}{N-1}\right)}-\frac{N-1}{2{\mathbf{\sigma }}^2}\mathrm{var}{\mathbf{x}}_{\backslash L}\right)>0,}$
SumXT23:	${\displaystyle \sum _{L=1}^N{x}_L\exp \left(-\frac{{\overline{\mathbf{x}}}_{\backslash L}^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+\frac{{\mathbf{\sigma }}^2}{N-1}\right)}-\frac{N-1}{2{\mathbf{\sigma }}^2}\mathrm{var}{\mathbf{x}}_{\backslash L}\right)>0,}$
SumXT123:	${\displaystyle \sum _{L=1}^N{x}_L\exp \left(-\frac{x_L^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+{\mathbf{\sigma }}^2\right)}-\frac{{\overline{\mathbf{x}}}_{\backslash L}^2}{2\left({\mathbf{\sigma }}_{\mathrm{s}}^2+\frac{{\mathbf{\sigma }}^2}{N-1}\right)}-\frac{N-1}{2{\mathbf{\sigma }}^2}\mathrm{var}{\mathbf{x}}_{\backslash L}\right)>0,}$