An advanced pulse-avalanche stochastic model of long gamma-ray burst light curves

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Table 2.

Optimised model parameter for the BATSE, Swift, and Fermi datasets.

Parameter	SS96–BATSE	B24–BATSE	B24–Swift	BATSE	Swift	Fermi
μ	1.20	$1 . 10_{- 0.02}^{+ 0.03}$ $1.10^{+0.03}_{-0.02}$	$1 . 34_{- 0.02}^{+ 0.03}$ $1.34^{+0.03}_{-0.02}$	$0 . 84_{- 0.03}^{+ 0.03}$ $0.84^{+0.03}_{-0.03}$	$1 . 06_{- 0.01}^{+ 0.02}$ $1.06^{+0.02}_{-0.01}$	$0 . 97_{- 0.07}^{+ 0.01}$ $0.97^{+0.01}_{-0.07}$
μ₀	1.00	$0 . 91_{- 0.07}^{+ 0.06}$ $0.91^{+0.06}_{-0.07}$	$1 . 16_{- 0.10}^{+ 0.18}$ $1.16^{+0.18}_{-0.10}$	$0 . 98_{- 0.1}^{+ 0.22}$ $0.98^{+0.22}_{-0.1}$	$1 . 24_{- 0.28}^{+ 0.20}$ $1.24^{+0.20}_{-0.28}$	$1 . 55_{- 0.19}^{+ 0.09}$ $1.55^{+0.09}_{-0.19}$
α	4.00	$2 . 57_{- 0.52}^{+ 0.07}$ $2.57^{+0.07}_{-0.52}$	$2 . 53_{- 0.01}^{+ 0.25}$ $2.53^{+0.25}_{-0.01}$	$9 . 62_{- 1.24}^{+ 0.03}$ $9.62^{+0.03}_{-1.24}$	$7 . 03_{- 0.64}^{+ 0.00}$ $7.03^{+0.00}_{-0.64}$	$3 . 85_{- 0.00}^{+ 0.56}$ $3.85^{+0.56}_{-0.00}$
δ₁	−0.50	$- 1 . 28_{- 0.05}^{+ 0.16}$ $-1.28^{+0.16}_{-0.05}$	$- 0 . 75_{- 0.29}^{+ 0.11}$ $-0.75^{+0.11}_{-0.29}$	$- 1 . 36_{- 0.10}^{+ 0.16}$ $-1.36^{+0.16}_{-0.10}$	$- 1 . 37_{- 0.08}^{+ 0.21}$ $-1.37^{+0.21}_{-0.08}$	$- 0 . 99_{- 0.19}^{+ 0.20}$ $-0.99^{+0.20}_{-0.19}$
δ₂	0	$0 . 28_{- 0.03}^{+ 0.01}$ $0.28^{+0.01}_{-0.03}$	$0 . 27_{- 0.02}^{+ 0.01}$ $0.27^{+0.01}_{-0.02}$	$0 . 08_{- 0.04}^{+ 0.10}$ $0.08^{+0.10}_{-0.04}$	$0 . 04_{- 0.03}^{+ 0.04}$ $0.04^{+0.04}_{-0.03}$	$0 . 03_{- 0.02}^{+ 0.01}$ $0.03^{+0.01}_{-0.02}$
τ_min (s)	0.02	$0 . 02_{- 0.01}^{+ 0.02}$ $0.02^{+0.02}_{-0.01}$	$0 . 03_{- 0.02}^{+ 0.02}$ $0.03^{+0.02}_{-0.02}$	$0 . 02_{- 0.01}^{+ 0.02}$ $0.02^{+0.02}_{-0.01}$	$0 . 02_{- 0.01}^{+ 0.03}$ $0.02^{+0.03}_{-0.01}$	$0 . 03_{- 0.01}^{+ 0.01}$ $0.03^{+0.01}_{-0.01}$
τ_max (s)	26.0	$40 . 2_{- 1.2}^{+ 0.9}$ $40.2^{+0.9}_{-1.2}$	$56 . 8_{- 1.3}^{+ 0.4}$ $56.8^{+0.4}_{-1.3}$	$33 . 15_{- 1.29}^{+ 0.06}$ $33.15^{+0.06}_{-1.29}$	$62 . 46_{- 2.82}^{+ 0.19}$ $62.46^{+0.19}_{-2.82}$	$35 . 84_{- 0.00}^{+ 0.87}$ $35.84^{+0.87}_{-0.00}$
α_BPL	–	–	–	$1 . 61_{- 0.11}^{+ 0.00}$ $1.61^{+0.00}_{-0.11}$	$1 . 89_{- 0.01}^{+ 0.03}$ $1.89^{+0.03}_{-0.01}$	$1 . 88_{- 0.09}^{+ 0.03}$ $1.88^{+0.03}_{-0.09}$
β_BPL	–	–	–	$2 . 19_{- 0.05}^{+ 0.08}$ $2.19^{+0.08}_{-0.05}$	$2 . 53_{- 0.10}^{+ 0.11}$ $2.53^{+0.11}_{-0.10}$	$2 . 58_{- 0.11}^{+ 0.06}$ $2.58^{+0.06}_{-0.11}$
F_break (10⁻⁷ erg cm⁻² s⁻¹)	–	–	–	$6 . 18_{- 0.20}^{+ 2.20}$ $6.18^{+2.20}_{-0.20}$	$3 . 44_{- 0.60}^{+ 0.10}$ $3.44^{+0.10}_{-0.60}$	$2 . 88_{- 0.20}^{+ 0.70}$ $2.88^{+0.70}_{-0.20}$
F_min (10⁻⁸ erg cm⁻² s⁻¹)	–	–	–	$4 . 87_{- 0.52}^{+ 1.16}$ $4.87^{+1.16}_{-0.52}$	$1 . 41_{- 0.04}^{+ 0.06}$ $1.41^{+0.06}_{-0.04}$	$6 . 04_{- 0.44}^{+ 0.48}$ $6.04^{+0.48}_{-0.44}$

Loss (Train best)	–	0.72	0.38	0.38	0.46	0.54
Loss (Train avg.)	–	0.98	0.66	0.84	0.89	0.94

Loss (Test)	1.47	0.88	0.56	0.49	0.55	0.61

Loss (Test: ⟨F/F_p⟩)	1.01	0.67	0.46	0.19	0.40	0.13
Loss (Test: ⟨(F/F_p)³⟩)	0.40	0.20	0.20	0.27	0.28	0.18
Loss (Test: ⟨ACF⟩)	2.24	0.64	0.49	0.38	0.71	0.58
Loss (Test: T_20%)	2.22	2.04	1.08	1.62	1.37	2.17
Loss (Test: S2N distr.)	–	–	–	0	0	0

Notes. Column 2 lists the parameters provided by SS96 for the BATSE dataset, while Columns 3 and 4 present the optimised parameters provided by B24 for BATSE and Swift/BAT, respectively. Columns 5, 6, and 7 report the optimised parameters for BATSE, Swift/BAT, and Fermi/GBM, respectively, obtained after 30 generations of the GA. The best-fitting values of the 11 parameters were determined as the medians of their distributions in the final generation, with uncertainties estimated from the 16th and 84th percentiles. “Train best” refers to the loss of the best-performing generation, while “Train avg”. represents the average loss in the final generation. The test set consists of a newly generated collection of 5000 simulated LCs, with the last five rows detailing the individual contributions to the “Test” loss.

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