"The equivalence test for Euclidean distance can be found in text book of Wellek (2010).[2] The equivalence test for the total variation distance is developed in Ostrovski (2017).[3] The exact equivalence test for the specific cumulative distance is proposed in Frey (2009).[4]"
found by chance (while looking at diagnostic for multinomial models) https://en.wikipedia.org/wiki/Multinomial_distribution#Equivalence_tests_for_multinomial_distributions
"The equivalence test for Euclidean distance can be found in text book of Wellek (2010).[2] The equivalence test for the total variation distance is developed in Ostrovski (2017).[3] The exact equivalence test for the specific cumulative distance is proposed in Frey (2009).[4]"