Find the complete statistic for Uniform(theta,theta+1)

Joyce Sharp

Joyce Sharp

Answered question

2022-09-24

Find the complete statistic for Uniform θ , θ + 1

Answer & Explanation

elilsonoulp2l

elilsonoulp2l

Beginner2022-09-25Added 9 answers

For the U ( θ , θ + 1 ) family of distributions, a minimal sufficient statistic is the pair of order statistics T = ( X ( 1 ) , X ( n ) ). But T is not a complete statistic because the range R = X ( n ) X ( 1 ) is an ancillary statistic. Note that R = ( X ( n ) θ ) ( X ( 1 ) θ ), which shows that the distribution of R is independent of θ, making it an ancillary statistic. As a result, E ( R ) = c is also free of θ and therefore you have a non-zero function of T whose expectation is zero:
E θ [ X ( n ) X ( 1 ) c ] = 0 , θ R
So the minimal sufficient statistic T is not complete, and when this happens we can say there is no complete statistic in the model

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?