Part-3, Q-3.6

Can anyone please explain why are we taking max|xi|, isn't |xi| enough ??

 

don't have the notes to hand, tho i do have exam papers, can you elaborate?

 

The likelihood function for the parameter Q based on a random sample of 'n'
observations from a population with a continuous uniform distribution on the range
(-Q / 2,Q / 2) is:

 

The density function for the data is
f(x,Q) = 1/2Q -Q <= x1, x2, x3…, xn <Q


So the likelihood is L(Q) = (1/2Q)^n

Since we can’t use calculus, we instead need to choose Q that maximises L(Q)

We need to choose the smallest value we can. But we need to satisfy the inequality above -Q <= x1, x2, x3…, xn <Q,

So the smallest Q we can choose is max |xi|

 

I think the density function should be 1/Q for -Q/2< xi < Q/2. So the likelihood function is (1/Q)^n.

 

You're right, my solution assumed data on the range (-Q, Q). For the range (-Q/2, Q/2) adjust accordingly.