Maximum Likelihood Estimator for a Gamma density in R

I just simulated 100 randoms observations from a gamma density with alpha(shape parameter)=5 and lambda(rate parameter)=5 :

x=rgamma(100,shape=5,rate=5)

Now, I want to fin the maximum likelihood estimations of alpha and lambda with a function that would return both of parameters and that use these observations.

Any hints would be appreciate. Thank you.

Solution

You can use fitdistr(...) for this in the MASS package.

set.seed(1)   # for reproducible example
x <- rgamma(100,shape=5,rate=5)

library(MASS)
fitdistr(x, "gamma", start=list(shape=1, rate=1))$estimate
#    shape     rate 
# 6.603328 6.697338

Notice that with a small sample like this you don't get great estimates.

x <- rgamma(10000,shape=5,rate=5)
library(MASS)    # may be loaded by default
fitdistr(x, "gamma", start=list(shape=1, rate=1))$estimate
#    shape     rate 
# 4.984220 4.971021

fitdistr(...) also returns the standard error of the estimates and the log-likelihood.