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Publication Number: FHWARD03041 
The following formulations for the combined skewness and kurtosis test were developed based on the reference [41].
For the skewness, we have:
Figure 76: Equation. Skewness definition.
For kurtosis, we have:
Figure 77: Equation. Kurtosis definition.
To evaluate the skewness and kurtosis tests results, the nondimensional skewness and kurtosis coefficients are computed, as following:
Figure 78: Equation. Nondimensional skewness coefficient definition.
Figure 79: Equation. Nondimensional kurtosis coefficient definition.
Based on the g_{1} and g_{2} values, the statistics _{ } and b_{2} are found next:
Figure 80: Equation. Definition of _{} statistic.
Figure 81: Equation. Definition of b_{2} statistic.
To find z_{1} value, the following parameters are computed using _{} and b_{2} statistics:
Figure 82: Equation. Definition of intermediate parameter A.
Figure 83: Equation. Definition of intermediate parameter B.
Figure 84: Equation. Definition of intermediate parameter C.
Figure 85: Equation. Definition of intermediate parameter D.
Figure 86: Equation. Definition of intermediate parameter E.
The corresponding z_{1} value used as a skewness test statistic is the following:
Figure 87: Equation. Definition of skewness test statistic z_{1}.
To find z_{2} value, the following intermediate parameters are computed next:
Figure 88: Equation. Definition of the mean of intermediate parameter meanb_{2}.
Figure 89: Equation. Definition of the variance of intermediate parameter varb_{2}.
Figure 90: Equation. Definition of intermediate parameter F.
Figure 91: Equation. Definition of intermediate parameter G.
Figure 92: Equation. Definition of intermediate parameter H.
The corresponding z_{2} value used as a kurtosis test statistic is the following:
Figure 93: Equation. Definition of kurtosis test statistic z_{2}.
The z_{1} and z_{2} statistics are used to obtain the pvalues (the probability that values of the standard normal distribution are more extreme than the computed z_{1} and z_{2} statistics).
Topics: research, infrastructure, pavements and materials Keywords: research, infrastructure, pavements and materials TRT Terms: PavementsUnited StatesTestingDatabases, PavementsPerformance, pavement layers Updated: 04/23/2012
