| Summary: | 碩士 === 國立中興大學 === 應用數學系 === 87 === We are adopting the concept of Locally Most Powerful test
and Locally Most Powerful Invariate test to derive optimal
tests with respect to one-sided for one unknown parameter and
two-sided for two unknown parameters problems,respectively.
In this thesis, the problem under discussion is that whether
a circular random sample is from the uniform distribution or
from Cardioid distribution. After these two respective optimal
tests have been developed, some optimal properties pertaining to
these tests are established, as well. Finally, the Monte-Carlo
simulation is carried out to obtain the numerical result of the
theoretical consequence, and the performance of simulation is
far better than what we have expected.
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