| Summary: | 碩士 === 淡江大學 === 水資源及環境工程學系 === 86 === The theoretical cumulative probability of the mixture
distributions shows reverse curvatures. For the real
hydrological data, however, due to the small sample size and the
characteristics of data, data that draw on the probability paper
often shows the reverse curvatures. By this time, it tends to
identify it to mixture distributions. Consequently, when the
data shows reverse curvatures on probability paper, would it
satisfy a single probability distribution or mixture
distributions is the major objection of this study. First of
all, the synthetic data which is statistical property is known
is fitted by mixture probability distribution (NOR, LN) and
single probability distribution (NOR, LN2, EV1 and PT3) to yield
estimated values separately. The difference between the
comparison of estimated value and theoretical value and the
comparison of estimated value and sample itself has been
discussed with the different sample sizes to examine the aptness
of the mixture distributions. Furthermore, the record of
hydrology data of Taiwan area, at least thirty years of the
annual maximum 1-day, 2-day, and 3-day rainfall (total 250
stations), is also analyzed in this study.From this research
result, the hydrology data inclined to be misidentified as a
mixture distribution because of property of the data and its
small sample. However, most of the cases are belonged to Type I
extreme distribution or Pearson typeⅢ distribution.For the
annual maximum 1-day, 2-day and 3-day rainfall data, it was
found that the mixture log-normal distribution is not
appropriate. The most appropriate distributions are Pearson Type
Ⅲ and mixture normal distributions for the real data. However
when the best distribution is mixture normal, most of the second
best one are Pearson Type Ⅲ distribution, particularly for the
small sample size. Therefore, according to the results obtained
by the synthetic data study, the Pearson Type Ⅲ distribution is
an appropriate for the annual maximum rainfall data in Taiwan
area.
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