If it is possible for repeated values to appear in the experimental results (e.g., because they come from a limited subset of natural numbers), is it impossible to use statistical tests that require the assumption of continuity of the distribution?
And if, for example, yi = round_to_integer{ f(xi) } and X has the probability distribution N(m,sigma)? Y is set of results.
@Jochen Wilhelm Thank you very much for your answer. However, the normal distribution is only an example here. Can the above observation be generalized to other continuous distributions, assuming the data are the result of a real experiment and their empirical distribution function does not resemble "vicious" theoretical distributions?
PS. Dear Professor Wilhelm, I even wanted to write in the question that I hoped (based on personal experience) for your answer, but I was worried about whether it was appropriate.
To make the problem useful to the wider community, I presented an example that wasn't consistent with my actual situation. I see I made a mistake. Therefore, I will briefly present my real-life example.
This experiment examines the effect of genetic algorithm parameters on the efficiency of finding the minimum of functions in different dimensions (here measured by the number of objective function calculations to achieve a given accuracy – yi). The parameters are: the crossover probability p_cross, the probability of general mutation p_mut_gen, and the probability of specific mutation p_mut_spec.
p_cross ~ uniform(0,1)
p_mut_gen ~ triangular (a=const, b, c=const) b
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