Read this. Pg 13-14
suppose that Y1,...Yn are random samples from a uniform distribtution with
f(y l θ ) = 1/ (2θ +1) for 0<y<2θ +1.
find the max likelihood for θ.
L = product of 1/ (2θ +1) n times
= [1/ (2θ +1) ]^n
taking ln and then differentiation, i get (-2n) / (2θ +1)
but if i set that to 0, i do not get an answer.
may i know what went wrong?
Point to remember: When the range of the variable depends upon the unknown parameter of the distribution, special care should be taken. Here, ; ie depends on . So, just a differentiation won't do the job.
Hint: Do you realize the fact that the pdf will be maximum when is minimum? Also, do you know what are "order statistics"?
ya i did realise that the pdf would be max when θ is min. i do not know what order stats are but based on wiki, i believe that if Yn is the largest among then it is greater than all other Yi of size n.
does that mean that P( Yn < fixed value ) = P(all Y < fixed value ) =[ Y/ (2θ +1) ] ^n
and then we differentiate [ Y/ (2θ +1) ] ^n to get the pdf? but i thought the pdf was already given in the question as 1/ (2θ +1)?
sorry, im new to this topic and am confused. thanks for helping