Consider the case of two random variables obeying log-normal distributions. Suppose that the $\mu$ parameters are equal but the $\sigma$ parameters aren't. This would imply that not only the variances-, but the skewness and kurthosis, etc., would also differ. Would this cause a problem if we were to apply the Brown–Forsythe test for the equality of variances? Would the p-value of the test be reliable?
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