R Under development (unstable) (2023-11-25 r85635 ucrt) -- "Unsuffered Consequences"
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> library(HyperbolicDist)
> 
> ### Gamma distribution
> k <- 4
> shape <- 2
> old <- 0
> new <- 1
> sampSize <- 1000000
> 
> ### Calculate 1st to 4th raw moments
> m <- numeric(k)
> for (i in 1:k){
+    m[i] <- gamma(shape + i)/gamma(shape)
+ }
> m
[1]   2   6  24 120
> 
> ### Calculate 4th moment about new
> momChangeAbout(k, m, old, new)
[1] 53
> ### Calculate 3rd about new
> momChangeAbout(3, m, old, new)
[1] 11
> 
> ### Calculate 1st to 4th moments about new
> momChangeAbout(oldMom = m, oldAbout = old, newAbout = new)
[1]  1  3 11 53
> momChangeAbout(order = "all", m, old, new)
[1]  1  3 11 53
> 
> ### Approximate kth moment about new using sampling
> x <- rgamma(sampSize, shape)
> mean((x - new)^k)
[1] 53.04206
> 
> 
> proc.time()
   user  system elapsed 
   0.40    0.06    0.40