Methods for Testing Normality of Hydrologic Time Series - Hydrologic Time Series Analysis: Theory and Practice - page 48

2 2

K 2 =

ZbZb

(10) 1 2

2 2

where

Zb are the standard normal deviates equivalent to
transformations of b (skewness) and b (kurtosis) (Armitage and Colton,
1998b). The test-statistic ( K 2 ) has approximately a chi-square distribution
with 2 degrees of freedom under the assumption that two summands [i.e.,
2

Zb and

( )

()

1

2

Zb are independent and the population is normally
distributed. The assumption of independence cannot be held up for small and
moderate sample sizes. Thus, the fact that K 2 is chi-distributed under the null
hypothesis does not hold true for the most common sample sizes. Test-statistics
of the DAP test is not easy to compute manually, and therefore, statistical
software may be used.

Zb and ( )

( ] 1

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