Unformatted text preview: # January 27, 2011 # calculation of MLE for Gamma distribution # illinois 1960 rainfall data (see chapter 10) # parametric bootstrap #observed MLE : lam.0 = 1.608263 alpha.0 = 0.354287 # a bootstrap to illustrate if the normal approximation is reasonable # n = 48 = length(rain.dat) # theta.hat = c(1.608263 , 0.354287)  lam.hat , alpha.hat # in this simulation we use fitdistr # instead of nlm. # It is similar but is numerically more stable # The parametric bootstrap will be for MLE and method of moments # The MLE is calculated using a numerical procedure. Earlier we used nlm # There is another program fitdistr # It fits several specific parametric models and is more stable than nlm # It is in the library or package MASS You may load this using # library(MASS) # or from the menu at the top of the RGUI # This example also shows that the distribution of the MLE is well approximated by a normal distribution when n = 48 # This particular Gamma distribution is very skewed, and a normal approximation seems to be quite good for n=48. # This particular Gamma distribution is very skewed, and a normal approximation seems to be quite good for n=48....
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 Spring '11
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