How does MATLAB compute p-values for Anderson Darling Test for the weibull distribution?

I have compared the reported p-values for the AD test across MATLAB and Minitab for a given dataset for the weibull distribution. The results match which is what I expected, but I need to know how the calculations are performed in the background?

There is very little literature that I could find that described how this process works for non-normal distributions.

Answer 1

[Yash]

Hello Sasan,

The Anderson-Darling (AD) test is a statistical test used to determine whether a given sample of data comes from a specific probability distribution. In MATLAB, the "adtest" function is used to perform the AD test. It calculates a test statistic and p-value by comparing the dataset's distribution to the expected one. If the p-value is less than a chosen significance level, we reject the idea that the data fits the expected distribution. If the p-value is higher, we fail to reject the idea that the data fits the expected distribution.

To know about the function you can refer to its documentation here: https://in.mathworks.com/help/stats/adtest.html

The p-value in MATLAB is calculated using the AD test statistic and the corresponding null distribution. The null distribution is the distribution of the AD test statistic under the null hypothesis that the sample data comes from the specified distribution. The p-value is then calculated as the probability of observing a test statistic as extreme or more extreme than the observed test statistic, assuming the null hypothesis is true.

You can refer to the "More about" section of its MATLAB documentation for more information on the function and the underlying algorithm: https://in.mathworks.com/help/stats/adtest.html#btq5i9_

Hope this helps!