Thanks for your sharing. I am new to such problems. Can you explain why the PDF of Xn and the value Y is to differentiate the probability with respect to Y?
Hi Bill, I have questions about Bias and MSE of the order statistics, especially for Uniform distribution. Do you have personal contract info? Or you can chat with me privately. Thx.
Hi there. For uniform distribution, naturally, your expectation should be spreading all the observations evenly. For example, if you have 3 observations for standard uniform, your expectation for the three observations should be 0.25, 0.5, 0.75. Another example, suppose you draw 7 observations from a uniform distribution from 21 to 29, what should be your expected values for the 7 observations? They should be 22, 23, 24 25, 26, 27, 28. By conjecture, you can see that for the i-th observation of n draws from a uniform distribution from (a,b), its expectation is a+(b-a)/(n+1)*i So you can see that the order statistics is unbiased for uniform distribution. I am not sure about MSE, will update you on that if I can think of anything.
