Distribution

Equation

Parameters

Log Likelihood

gamma-Pareto

(1)

$c=0.232$ ; $\theta =0.081$ ; $\alpha =19.43$

−36,070.22

gamma-Pareto R-truncated

(25)

$c=0.222$ ; $\theta =0.087$ ; $\alpha =20.03$ ; $x_u=450$

−36,093.94

bi-truncated gamma-Pareto

(29)

$c=0.227$ ; $\theta =0.087$ ; $\alpha =19.56$ ; $x_l=0.09$ ; $x_u=450$

−36,093.07

gamma-Pareto II

(18)

$c=0.35$ ; $\theta =1.944$ ; $\alpha =4.7$

−35,766.08

bi-truncated gamma-Pareto II

(33)

$c=0.35$ ; $\theta =1.944$ ; $\alpha =4.7$ ; $x_l=0.09$ ; $x_u=450$

−35,762.30

lognormal

(16)

$m=7.496$ ; $\sigma =0.983$

−36,099.25

double Pareto lognormal

(17)

$\alpha =2.981$ ; $\beta =3$ ; $\mu =2.025$ ; $\sigma =0.979$

−36,166.91