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
> set.seed(1234)
> nsample <- 10
> 
> #Poisson
> 
> x <- rpois(nsample, lambda=7.5)
> L2 <- function(lam)
+   (qpois(1/2, lambda = lam) - median(x))^2
> curve(L2(x), 5, 9, xlab=expression(lambda), ylab=expression(L2(lambda)), main="squared differences", n=201)
> 
> fitdist(x, "pois", method="qme", probs=1/2, start=list(lambda=2), control=list(trace=1, REPORT=1))
initial  value 36.000000 
iter   1 value 36.000000
final  value 36.000000 
converged
Fitting of the distribution ' pois ' by matching quantiles 
Parameters:
       estimate
lambda        2
> fitdist(x, "pois", method="qme", probs=1/2, start=list(lambda=6.8), control=list(trace=1, REPORT=1))
initial  value 1.000000 
iter   1 value 1.000000
final  value 1.000000 
converged
Fitting of the distribution ' pois ' by matching quantiles 
Parameters:
       estimate
lambda      6.8
> fitdist(x, "pois", method="qme", probs=1/2, start=list(lambda=15), control=list(trace=1, REPORT=1))
initial  value 49.000000 
iter   1 value 49.000000
final  value 49.000000 
converged
Fitting of the distribution ' pois ' by matching quantiles 
Parameters:
       estimate
lambda       15
> 
> fitdist(x, "pois", method="qme", optim.method="SANN", probs=1/2, start=list(lambda=2), control=list(trace=1, REPORT=100))
sann objective function values
initial       value 36.000000
iter     1000 value 0.000000
iter     2000 value 0.000000
iter     3000 value 0.000000
iter     4000 value 0.000000
iter     5000 value 0.000000
iter     6000 value 0.000000
iter     7000 value 0.000000
iter     8000 value 0.000000
iter     9000 value 0.000000
iter     9999 value 0.000000
final         value 0.000000
sann stopped after 9999 iterations
Fitting of the distribution ' pois ' by matching quantiles 
Parameters:
       estimate
lambda 8.425269
> fitdist(x, "pois", method="qme", optim.method="SANN", probs=1/2, start=list(lambda=17), control=list(trace=1, REPORT=100))
sann objective function values
initial       value 81.000000
iter     1000 value 0.000000
iter     2000 value 0.000000
iter     3000 value 0.000000
iter     4000 value 0.000000
iter     5000 value 0.000000
iter     6000 value 0.000000
iter     7000 value 0.000000
iter     8000 value 0.000000
iter     9000 value 0.000000
iter     9999 value 0.000000
final         value 0.000000
sann stopped after 9999 iterations
Fitting of the distribution ' pois ' by matching quantiles 
Parameters:
       estimate
lambda 8.183321
> 
> 
> 
> #Geometric
> 
> x <- rgeom(nsample, 1/3)
> L2 <- function(p)
+   (qgeom(1/2, p) - median(x))^2
> curve(L2(x), 0.10, 0.95, xlab=expression(p), ylab=expression(L2(p)), main="squared differences", n=301)
> 
> fitdist(x, "geom", method="qme", probs=1/2, start=list(prob=1/2), control=list(trace=1, REPORT=1))
initial  value 16.000000 
iter   2 value 4.000000
iter   2 value 4.000000
iter   2 value 4.000000
final  value 4.000000 
converged
Fitting of the distribution ' geom ' by matching quantiles 
Parameters:
     estimate
prob    0.276
> fitdist(x, "geom", method="qme", probs=1/2, start=list(prob=1/20), control=list(trace=1, REPORT=1))
initial  value 81.000000 
iter   1 value 81.000000
final  value 81.000000 
converged
Fitting of the distribution ' geom ' by matching quantiles 
Parameters:
     estimate
prob     0.05
> 
> proc.time()
   user  system elapsed 
   7.15    0.25    7.40