eldo_user

Monte Carlo Analysis
Additional Uncertainty Analyses (the .mcm File)
==> Scale and Shape:
Mu ... Maximum Likelihood (ML) Estimation to the Mean
Sigma ... ML Estimation to the Standard Deviation
Skewness ... Third Central Moment Divided by the Cube of Sigma
Kurtosis ... Fourth Central Moment Divided by Fourth Power of Sigma
(Sample Skewness and Kurtosis are Corrected for Bias)
Index
Name
of Meas Mu Sigma Skewness Kurtosis of Meas
----------------------------------------------------------------------------
1 8.38289e-01 9.93480e-03 -5.07100e-02 2.90190e+00 MAX
2 2.19635e+00 5.09067e-03 -3.76104e-02 2.90041e+00 BW
3 -5.44169e-02 1.96232e-04 -3.38857e-02 3.17208e+00 IVDD
D’Agostino-Pearson Test of Normality
We provide the test of normality of D’Agostino-Pearson K 2 (K-squared test) based on the
skewness and kurtosis coefficients. When these two numbers are different from the reference
value, one may conclude that the empirical distribution is not compatible with the normal law.
As the number of samples increase this test becomes particularly efficient when n ≥ 20, and is
better than the Kolmogorov-Smirnov test. The idea is relatively simple. One tries to center and
reduce the skewness and kurtosis indicators to obtain two statistics z 1 and z 2 . And one can prove
that the statistics z 1 and z 2 are asymptotically normal. The D’Agostino-Pearson statistic is the
combination:
If the null hypothesis of normality is true, then K 2 is approximately distributed as the χ 2
distribution with two degrees of freedom. Given a significance level α, the hypothesis regarding
the normality is rejected if the test statistic satisfies:
Tip
For an instructive introduction to this test see: R. B. D’Agostino, A. Belanger and R. B.
D’Agostino Jr, A suggestion for Using Powerful and Informative tests of Normality. The
American Statistician, Vol 44, No 4. (1990), pp. 316-321.
The results of this test are organized as classical hypothesis tests, see Hypothesis Tests section
for more information.
498
Eldo® User's Manual, 15.3