Astronomy & Astrophysics

Table 1: Performance ordering of the statistics (Eqs. (12)-(17)), based on the average chi square distance between true and estimated models. The notation $A \succ B$ indicates here that $\langle d_{\chi^2} \rangle_A < 0.95 \langle d_{\chi^2} \rangle_B$ , and $A \succsim B$ indicates that $0.95 \langle d_{\chi^2} \rangle_B < \langle d_{\chi^2} \rangle_A < \langle d_{\chi^2} \rangle_B$ . The labels "e.s.'' and "e.c.'' refer to "equal size'' and "equal count'' bins, respectively. ${\cal N}_{\rm bg} = 50$ .
Table 2: Similar to Table 1, but using the area under the receiver-operator curve (Fig. 3) as a measure of performance. ${\cal N}_{\rm bg} = 50$ .
Table 3: Maximum-L parameters deduced from XMM-Newton observations of the TMC. Superscripts a) and b) refer to different observations of the same object; $T_{\rm exp}$ is the exposure time, and $N_{\rm cnt}$ is the observed number of counts (corresponding to ${\cal N}_{\rm src} + {\cal N}_{\rm bg}$ ). Errors outside brackets represent projections of the 68% likelihood surfaces (Fig. 11 inlets); errors in brackets are obtained from Monte-Carlo simulations (Sect. 6.3). Luminosities L_X refer to $N_{\rm H}$ = 0 and the energy band from 0.3 to 10 keV.