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> require("fitdistrplus")
Loading required package: fitdistrplus
Loading required package: MASS
Loading required package: survival
> require("actuar")
Loading required package: actuar

Attaching package: 'actuar'

The following objects are masked from 'package:stats':

    sd, var

The following object is masked from 'package:grDevices':

    cm

> 
> set.seed(1234)
> 
> n <- 1e3
> x <- rfpareto(n, 1, 2, 2, 2, scale=2)
> 
> fitdistrplus:::startarg_fellerpareto_family(x, "pareto4")
$min
[1] 1.281281

$shape1
[1] 1.970823

$shape2
[1] 2.278414

$scale
[1] 2.62346

> 
> fitdistrplus:::startarg_fellerpareto_family(x, "pareto3")
$min
[1] 1.281281

$shape
[1] 2.682464

$scale
[1] 1.741837

> 
> fitdistrplus:::startarg_fellerpareto_family(x, "pareto2")
$min
[1] 1.281281

$shape
[1] 1.362517

$scale
[1] 1.735447

> 
> fitdistrplus:::startarg_fellerpareto_family(x, "pareto1")
$shape
[1] 1.117406

$min
[1] 1.281281

> 
> fitdistrplus:::startarg_fellerpareto_family(x, "pareto")
$shape
[1] 0.9551719

$scale
[1] 1.735447

> 
> fitdistrplus:::startarg_fellerpareto_family(x, "llogis")
$shape
[1] 2.942622

$scale
[1] 4.759425

> 
> eps <- 1e-3
> fitdist(x, "pareto4", control=list(trace=1), lower=eps, optim="L-BFGS-B")
iter   10 value 1.529529
final  value 1.529404 
converged
Fitting of the distribution ' pareto4 ' by maximum likelihood 
Parameters:
       estimate Std. Error
min    1.294690  0.0458557
shape1 1.767942  0.3169416
shape2 2.276174  0.1644341
scale  2.423030  0.2591305
> fitdist(x, "pareto3", lower=eps, optim="L-BFGS-B")
Fitting of the distribution ' pareto3 ' by maximum likelihood 
Parameters:
      estimate Std. Error
min   1.089438 0.09145439
shape 3.057421 0.18634948
scale 1.945098 0.10440510
> #fitdist(x, "pareto2", lower=eps, optim="L-BFGS-B")
> #fitdist(x, "pareto1", lower=eps, optim="L-BFGS-B")
> #fitdist(x, "pareto", lower=eps, optim="L-BFGS-B")
> 
> fitdist(x, "llogis", lower=0, optim="L-BFGS-B")
Fitting of the distribution ' llogis ' by maximum likelihood 
Parameters:
      estimate Std. Error
shape 4.869676 0.12804791
scale 3.084787 0.03488625
> 
> 
> fitdistrplus:::startarg_fellerpareto_family(x, "fpareto")
$min
[1] 1.281281

$shape1
[1] 4.817928

$shape2
[1] 2.064787

$shape3
[1] 5.237083

$scale
[1] 1.557258

> 
> fitdist(x, "fpareto", lower=eps, optim="L-BFGS-B")
Fitting of the distribution ' fpareto ' by maximum likelihood 
Parameters:
        estimate Std. Error
min    1.3164080 0.03684752
shape1 1.3418349 0.50096115
shape2 2.7071309 0.61945382
shape3 0.7578861 0.25074530
scale  2.3323396 0.22466516
> 
> fitdistrplus:::startarg_fellerpareto_family(x-1, "trbeta")
$shape1
[1] 5.704643

$shape2
[1] 2.001012

$shape3
[1] 9.109486

$scale
[1] 1.233544

> 
> fitdist(x-1, "trbeta", lower=eps, optim="L-BFGS-B")
Fitting of the distribution ' trbeta ' by maximum likelihood 
Parameters:
       estimate Std. Error
shape1 2.686389  1.5104112
shape2 1.753533  0.5833188
shape3 2.516105  1.4498796
scale  2.129095  0.2608336
> 
> 
> fitdistrplus:::startarg_fellerpareto_family(x-1, "genpareto")
$shape1
[1] 4.533974

$shape2
[1] 13.03459

$scale
[1] 0.6603603

> 
> fitdist(x-1, "genpareto", lower=eps, optim="L-BFGS-B")
Fitting of the distribution ' genpareto ' by maximum likelihood 
Parameters:
       estimate Std. Error
shape1 7.190797  1.0520267
shape2 6.967985  0.9893185
scale  2.104492  0.6204669
> 
> fitdistrplus:::startarg_fellerpareto_family(x-1, "paralogis")
$shape
[1] 0.6901228

$scale
[1] 2.662399

> 
> fitdist(x-1, "paralogis", lower=eps, optim="L-BFGS-B")
Fitting of the distribution ' paralogis ' by maximum likelihood 
Parameters:
      estimate Std. Error
shape 2.458776 0.05093665
scale 3.308345 0.05986795
> 
> 
> x <- rfpareto(n, 0, 1, 2, 2, scale=2)
> 
> fitdistrplus:::startarg_fellerpareto_family(x, "invburr")
$shape1
[1] 11.76437

$shape2
[1] 1.791445

$scale
[1] 1.529135

> fitdistrplus:::startarg_fellerpareto_family(x, "invpareto")
$shape
[1] 1.440887

$scale
[1] 0.3434468

> fitdistrplus:::startarg_fellerpareto_family(x, "invparalogis")
$shape
[1] 1.203247

$scale
[1] 0.2772426

> 
> 
> proc.time()
   user  system elapsed 
   3.29    0.25    3.48