I have seen the questions like Correlations with unordered categorical variables , but I cannot implement the chi-square test since I don't have a chi-square table representing joint distribution. Besides, It was said that distance metrics like Euclidean distance is not reasonable. Currently, I just have several 1*n data, which are discrete variables or I can use their Gumbel softmax distribution approximation.
How can I test the association of those unordered category distributions? PS: For example, one data is [0.1 0.5 0.3 0.1], another one is [0.2 0.5 0.1 0.2]. Actually, they are quite similar if we sort them and compare them.