I'm studying for a stats exam and have many questions. Here's the first.
When finding the MLE for non-differentiable functions, you write down the pdf, then the likelihood function L(u), then, if that's a different value depending on the value of the parameter of interest (u), you use a graphical method.
Do you simply draw the graph and show that L(u) is highest at some value of x? And that is your MLE?
I am also wondering why the Exponential distribution is undifferentiable, but the Poisson is not? The Poisson is also only for values of u>0.
Please explain! Ta,