[SOLVED] Inverse of gamma function with R

Inverse of gamma function with R

With gamma() in R you get output 24 from input 5. How can I make inverse function which can get output 5 from input 24?

>gamma(5)
24

I found [invgamma] package, but I can’t understand if it is appropriate one nor how to use it…

Solution

Use uniroot to find the root of gamma(x) - a, where a is your number.

invgamma <- function(a, tol = .Machine$double.eps^0.5) {
  uniroot(\(x) gamma(x) - a, c(1, 1e2), extendInt = "upX", tol = tol)
}

invgamma(24)$root
#> [1] 5

invgamma(24)
#> $root
#> [1] 5
#> 
#> $f.root
#> [1] -5.207212e-11
#> 
#> $iter
#> [1] 19
#> 
#> $init.it
#> [1] NA
#> 
#> $estim.prec
#> [1] 7.450582e-09

^{Created on 2024-09-29 with reprex v2.1.0}

You can vectorize this function.

igamma <- Vectorize(invgamma, "a")
igamma(c(6, 24, 120)) |> t()
#>      root f.root        iter init.it estim.prec  
#> [1,] 4    -2.771117e-13 17   NA      7.450582e-09
#> [2,] 5    -5.207212e-11 19   NA      7.450582e-09
#> [3,] 6    2.727063e-11  18   NA      7.450583e-09

^{Created on 2024-09-29 with reprex v2.1.0}