R中Gamma密度的最大似然估计

Question

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.

Answer 1

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.