For example i have this data:
x-c(73,6,77,81,91,120,150,61,65,68,18,20,23,12,14,18,23,26
+26,27,2,3,3,40,41,41,6,10,11,12,37,38,38,6,73,6,51)
and i want to calculate the a=shape and b=scale parameters of gamma distribution. I want to solve this non-linear system
a*b=m1
a*b^2+(a^2)*(b^2)=m2
The m1 and m2 are these:
m1<-sum(x)/length(x)
m2<-sum((x)^2)/length(x)
I can solve it with hand and with calculator, but i wanna know how to instantly solve this with R
R can do this quite easily
library(nleqslv)
f <- function(x) {
a<-x[1]
b<-x[2]
c(a*b-m1,a*b^2+(a^2)*(b^2)-m2)
}
nleqslv(c(1,30), f)
Output should look like:
$`x`
[1] 1.286486 30.595840
$fvec
[1] -9.663381e-13 -1.396074e-10
$termcd
[1] 1
$message
[1] "Function criterion near zero"
$scalex
[1] 1 1
$nfcnt
[1] 11
$njcnt
[1] 2
$iter
[1] 10
You can make things more robust by providing gradients. Of course R can also estimate parameters for the gamma distribution directly (e.g. fitdistr from the MASS package).