Task 4. Anderson-Darling Test

The Anderson-Darling test statistic is defined as:

$\begin{array}{l}A^2 = -N -S\end{array}$

where

$\begin{array}{l}S = \sum_{i=1}^{N} \frac{2i-1}{N}[lnF(Y_i) + ln(1-F(Y_N_+_1_-_i))]\end{array}$

where $\begin{array}{l}F\end{array}$ is the cumulative distribution function of the probability model, $\begin{array}{l}i\end{array}$ is the rank of the data, and $\begin{array}{l}N\end{array}$ is the number of data points.

Copy the sheet titled Data and name the new sheet A-D Test.
Compute the cumulative frequency denoted by $\begin{array}{l}F(y_i)\end{array}$ .
Compute the cumulative frequency denoted by $\begin{array}{l}F(y_N_+_1_-_i)\end{array}$ .

Use the Excel function VLOOKUP to determine the CDF value at discharge index N + 1 - i, $\begin{array}{l}F(Y_N_+_1_-_i)\end{array}$ . The complete formula is shown below.

Question: What is the computed Anderson-Darling test statistic, $\begin{array}{l}A^2\end{array}$ ?

First, calculate $\begin{array}{l}S_i\end{array}$ for each discharge value. Next, compute the sum of the $\begin{array}{l}S_i\end{array}$ column. Finally, compute the Anderson-Darling test statistic, $\begin{array}{l}A^2\end{array}$ .

The computed Anderson-Darling test statistic is 0.706. This matches the value from Distribution Fitting Test 20 in the HEC-SSP Examples.

If time allows, continue to Task 5. Bayesian Information Criterion.