R Under development (unstable) (2024-07-10 r86888 ucrt) -- "Unsuffered Consequences"
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> library(fitdistrplus)
Loading required package: MASS
Loading required package: survival
> library(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 <- rtrgamma(n, 2, 2, scale=2)
> 
> fitdistrplus:::startarg_transgamma_family(x, "trgamma")
$shape1
[1] 7.953247

$shape2
[1] 1.002587

$scale
[1] 0.3374842

> 
> fitdistrplus:::startarg_transgamma_family(x, "gamma")
$shape
[1] 7.953247

$rate
[1] 0.3374842

> 
> fitdistrplus:::startarg_transgamma_family(x, "weibull")
$shape
[1] 3.081294

$scale
[1] 3.015039

> 
> fitdistrplus:::startarg_transgamma_family(x, "exp")
$rate
[1] 0.372565

> 
> fitdist(x, "trgamma")
Fitting of the distribution ' trgamma ' by maximum likelihood 
Parameters:
       estimate Std. Error
shape1 2.143840  0.4835707
shape2 1.974504  0.2516188
scale  1.932572  0.3420543
> fitdist(x, "gamma")
Fitting of the distribution ' gamma ' by maximum likelihood 
Parameters:
      estimate Std. Error
shape 7.372872  0.3225398
rate  2.746763  0.1243473
> fitdist(x, "weibull")
Fitting of the distribution ' weibull ' by maximum likelihood 
Parameters:
      estimate Std. Error
shape 3.038278 0.07291534
scale 3.004382 0.03301925
> fitdist(x, "exp")
Fitting of the distribution ' exp ' by maximum likelihood 
Parameters:
     estimate Std. Error
rate 0.372565 0.01178145
> 
> 
> #weird examples
> x <- rep(1, n)
> 
> fitdistrplus:::startarg_transgamma_family(x, "gamma")
$shape
[1] 1

$rate
[1] 1

> 
> #previous code
> n <- length(x)
> m <- mean(x)
> v <- (n - 1)/n*var(x)
> list(shape=m^2/v, rate=m/v)
$shape
[1] Inf

$rate
[1] Inf

> 
> 
> #normal -> weibull
> x <- abs(rnorm(n = 20, mean = 150, sd = 10))
> m <- mean(log(x))
> v <- var(log(x))
> shape <- 1.2/sqrt(v)
> scale <- exp(m + 0.572/shape)
> s1 <- list(shape=shape, scale=scale)
> cdfcomp(fitdist(x, "weibull", start=s1))
> 
> 
> proc.time()
   user  system elapsed 
   2.12    0.25    2.36