| Summary: | 碩士 === 國立東華大學 === 應用數學研究所 === 84 === To estimate an unknown distribution function F(x), the
empirical distribution function Fn(x) is a very popular choice.
If we are dealing with acontinuous and symmetric distribution,
then Schuster (1975) proposed anestimator Gn^(x) which shows
good performance, but the performance depends a great deal on
the estimator of the unknown center of symmetry. But if
theunderlying distribution is skewed, Gn^(x) is not appropriate.
We would like to propose a good estimator for F(x) when we have
littleinformation about the population where our data come from.
'Adaptive' idea wasused which first classifies the data as being
symmetric or asymmetric and in the symmetric case as light,
medium or heavy tailed and then Gn^(x) with appropriate
estimator of center or Fn(x) is used to estimate F(x). Monte
Carlostudies were carried out which showed that our estimator is
worth recommending.
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