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STAT 801
Problems: Assignment 6
- Suppose
are independent Poisson(
)
variables. Find the UMP level
test of
versus
and evaluate the constants for the case n=3 and
. - Suppose X has a Gamma(
) distribution with shape
parameter
known. Find the UMPU test of
and
evaluate the constants for the case
and
. - Suppose
are iid exponential(
).
- Find the exact confidence levels of 95% intervals based on normal
approximations to the distributions of the pivots
,
, and
for n=10, 20 and 40. - Find the shortest exact 95% confidence interval based on
; get numerical values for n=10, 20 and 40. - Find the exact confidence level of 95% confidence intervals based
on the chi-squared approximation to the distribution of deviance drop.
Compare the results with the previous question based on length and
coverage probabilities.
Figure out how to make a convincing comparison. Which method is better?
- Page 398. Q 1.
- Page 398 Q 2.
- Page 398. Q 6.
Richard Lockhart
Tue Apr 15 22:46:17 PDT 1997