# Max Likelihood Methods (Estimators)

Not what you're looking for? Search our solutions OR ask your own Custom question.

Let Y1<Y2<......<Yn be the order statistics of a random sample of size n from the uniform distribution of the continuous type over the closed interval [theta- rho, theta+ rho]. Find the maximum likelihood estimators for theta and rho. Are these two unbiased estimators?

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:13 pm ad1c9bdddfhttps://brainmass.com/statistics/maximum-likelihood-estimation/max-likelihood-methods-estimators-35066

#### Solution Preview

Please see attachment.

6.4.5 Let Y1<Y2<......<Yn be the order statistics of a random sample of size n from the

uniform distribution of the continuous type over the closed interval [theta- rho, theta+ rho]. Find the maximum likelihood estimators for theta and rho. Are these two unbiased estimators?

Answers:

MLE for theta (Y1+Yn)/2

For rho (Yn-Y1)/2

No

Solution. Since Y1<Y2<......<Yn are the order statistics ...

#### Solution Summary

The expert examines max likelihood methods using estimators.

$2.49