MLE and log likelihood function

[Rubaiyat Rahman]

Here, Y = {y1, y2, ..., y10} = {10, 9, 21, 4, 14, 11, 22, 9, 6, 4}. Using the (log-)likelihood function, how I can demonstrate the maximum likelihood estimation in STATA ?

[Rubaiyat Rahman]

I did as follows, but I am getting error

clear
set more off
matrix define Y = (10\9\21\4\14\11\22\9\6\4)
matrix list Y
svmat Y, names(y)
rename y1 y

capture program drop binomial
program define binomial
args llk theta
quietly replace `llk' = ( y*ln(`theta') ) + ( (10-y)*ln(1-`theta') )
end

ml model lf binomial (y=)
ml search
ml max
ml graph

[German Rodriguez]

The binomial distribution models the number of successes y out of n trials. Your y vector has entries between 4 and 22, but in the log-likelihood you specify n as 10. Clearly the data are not consistent with the model. If you change 10 to something like 25 the code will run and give the correct estimate of 0.44. You could also define a variable n to hold the binomial denominators, specify both y and n in your model statement, and use the macros $ML_y1 and $ML_y2 to refer to them when you evaluate the log-likelihood.