Table 1:

Slope s of a power law fit ( ) of the  - P diagram with and without the assumption of the DLR (Eq. (8)) for pulses.

(erg s-1)	s (with DLR)	s (without DLR)
1051	0.27	0.091
1050.5	0.24	0.093
1050	0.22	0.096
(erg s-1)
1053.5	0.24	0.093
1054	0.22	0.096
2.0	0.27	0.081
1.5	0.27	0.096
(keV)
400	0.33	0.089
600	0.33	0.088
800	0.33	0.096
0.3	0.27	-
0.6	0.22	-
1.0	0.15	-
1.5	0.09	-
Threshold
:2	0.30	0.11
x2	0.24	0.085

Notes. In the six blocks we respectively vary the lower (i); and upper (ii) limits of the pulse luminosity function; (iii) the slope of the luminosity function; (iv) the central value of a log-normal distribution for ; (v) the dispersion of the DLR; (vi) the detection threshold. The first row corresponds to our reference case with  erg s ^-1,  erg s^-1, ,  dex. It also assumes the validity of the Amati-like relation (Eq. (7)) with a dispersion of 0.3 dex and adopts the threshold criterion for BATSE given by Band (2003). In each block only one parameter is varied, the others keeping the values corresponding to the reference case.