Table 2
Two-parameter correlations involving optical luminosities and fluxes.
| X | Y | m | q | σ | ρ | K | R |
|
|
|||||||
| L × trest |
|
0.65 ± 0.03 | –0.39 ± 2.52 | 0.59 ± 0.01 | 0.64 | 0.47 | 0.72 |
| L × trest | E γ,iso | 0.78 ± 0.05 | –4.42 ± 4.99 | 0.58 ± 0.03 | 0.72 | –0.49 | 0.80 |
| t rest,PL | L end,PL | –0.83 ± 0.14 | 8.64 ± 1.36 | 0.84 ± 0.06 | -0.66 | –0.51 | –0.65 |
| t obs,PL | L end,PL | –0.77 ± 0.18 | 8.81 ± 2.35 | 0.90 ± 0.07 | –0.55 | –0.41 | –0.55 |
| t rest,PK | L end,PK | –1.40 ± 0.13 | 10.47 ± 0.81 | 0.92 ± 0.04 | –0.79 | –0.64 | –0.77 |
| t obs,PK | L end,PK | –1.32 ± 0.20 | 10.86 ± 0.75 | 1.08 ± 0.06 | –0.66 | –0.48 | –0.67 |
| t obs,PL | F PL | –0.48 ± 0.10 | –12.09 ± 1.19 | 0.65 ± 0.03 | –0.39 | –0.26 | –0.53 |
| t obs,PK | F PK | –0.93 ± 0.08 | –10.14 ± 0.72 | 0.69 ± 0.02 | –0.78 | –0.62 | -0.71 |
Notes. From left to right: X and Y parameters to be correlated (the best-fitting law reads log (Y) = q + mlog (X)); best-fitting parameters as obtained accounting for the sample variance (D’Agostini 2005): slope (m), normalization (q), intrinsic scatter (σ); errors are given at 95% c.l. The last three columns list the value of the Spearman rank (ρ), Kendall coefficient K, and R-index r statistics.
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