Distribution

Equation

Parameters

$\langle E\rangle$ (GeV)

${\chi }^2$

gamma-Pareto

(38)

$\varphi =2110$ ; $c=0.428$ ; $\theta =0.057$ ; $\alpha =6.716$

2.456

113.05

gamma-Pareto R-truncated

(39)

$\varphi =2106$ ; $c=0.429$ ; $\theta =0.057$ ; $\alpha =6.687$ ; $x_u=393587$

2.443

113.09

bi-truncated gamma-Pareto

(40)

$\varphi =2301$ ; $c=0.455$ ; $\theta =0.117$ ; $\alpha =5.039$ ; $x_l=0.212$ ; $x_u=393587$

2.518

101.06

gamma-Pareto II

(41)

$\varphi =2696$ ; $c=0.544$ ; $\theta =1.395$ ; $\alpha =1.34$

2.6

62.204

bi-truncated gamma-Pareto II

(42)

$\varphi =2373$ ; $c=0.544$ ; $\theta =1.4$ ; $\alpha =1.33$ ; $x_l=0.212$ ; $x_u=2373$

2.956

62.205

lognormal

(43)

$\varphi =10442$ ; $m=4.43\times {10}^{-3}$ ; $\sigma =2.787$

0.215

284.55

double Pareto lognormal

(44)

$\varphi =4992$ ; $\alpha =1.777$ ; $\beta =0.147$ ; $\mu =1.355$ ; $\sigma =0.654$

1.413

72.94