BOOTSTRAP

例

燈泡通常在使用1200小時後更換

檢驗二十個燈泡，其壽命X1-X20如下

1354 1552 1766 1325 2183 1354 1299
695  2586 2420 71 2195 1825
159 1577 3725 884  1014 965

想求壽命大於1200 小時之機率的信賴區間

If X ~exponential), then the MLE and MME is

=0.444

=13/20

resample from above data :

repeat the resampling B times

find 90% of the falls between 0.356 and 0.514

If =0.9, then

,

The same conclusion for =0.9,

Then

Both and are negative, shows that is not a good estimator,

i.e., exponential model does not fits well.