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Thank you for making your 2D KS implementation code public!

TL;DR: For many applications, it would be helpful to decrease the default prec parameter in the Qks function to a value below 1e-17, instead of the current 1e-06.

In the field that I work in (astronomy), it is common to report significance in terms of the number of standard deviations away from the mean of a Normal distribution. A significance level of at least 5σ is standard practice for rejecting null hypotheses. For example, a 5σ significance correspond to a p-value of 5.733e-07.

2DKS calculates the equivalent p-value for the 2D KS test in the Qks function. The default precision in the convergence criterion is 1e-06, which means that the function exits and reports a p-value of 0 for equivalent significances above ~4.6σ. For many physics and astronomy applications, it would be very helpful to decrease the default prec parameter to a lower value.

I tested the code with a range of input values and the function Qks converges well with the default 100 iterations and prec=1e-17. This would ensure 2DKS reports accurate p-values even for very high significance scenarios.

Thank you!

Hello,
first thank you very much for this implementation, I have looked for something similar for a very long time and this will help me a lot in my master's thesis (of course I have given credit to you for the code). I have a few questions regarding how to understand the results of two tests I have done on populations:

1. A and B
2. A and C (C is a subset of B)

The results I got are, respectively:

1. (0.07785494519464609, 0.0)
2. (0.17752050146508203, 0.0)

For both prob = 0, so I can obviously reject the null hypothesis. But can I refer to this value as the p-value like when I do an univariate K-S test? Also, can I understand the difference in D value, that distribution of C is more different from A than B? Finally, does the D in your code refer to D_BKS or Z_n in the original Foseno-Franceschini paper, or to another value?

Thank you in advance for your help.

Best regards
Przemek