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data often have positive skewness. Therefore, statistical properties including
only the mean and standard deviation or variance are not sufficient for the
studies related to water resources development and management. This is because
of the fact that the mean and standard deviation alone may not describe the
properties of the majority of the data values very well when the data are
skewed. Also, both the mean and the standard deviation are inflated by outlier
observations. Robust summary statistics, such as the median and other
percentile values have greater applicability to the skewed hydrologic data.
The skewed data are questionable regarding the applicability of hypothesis
(parametric) tests, which are based on the assumptions that the time series
data follow a normal distribution. These parametric tests may be of questionable
value when applied to hydrologic time series, as the time series are often
neither normal nor even symmetric (Helsel and Hirsch, 2002).
2.3.1 Classical Measure of Skewness
The 'coefficient of skewness ( g )' is the most common measure of skewness.
It is defined as the adjusted third moment about the mean divided by the cube
of the standard deviation ( s ), and is mathematically expressed as follows:
n
3
n
xx
Ç
i
g =
(16)
n
1
n
2
3
s
i
1
Fig. 2.4. Probability density function of a lognormal distribution.
 
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