Triangular fuzzification of random variables and power of distribution tests: Empirical discussion
A fuzzifying process of finitely valued random variables by means of triangular fuzzy sets is analyzed. Empirical studies show that if the random variable takes on a small number of different values, the one-sample test about the (fuzzy) mean of the fuzzified random variable is frequently more powerful than the classical test about the mean of the original random variable. This empirical conclusion is theoretically supported as follows: whenever the number of different values of a random variable X X is up to 4, the mean of the fuzzified random variable captures the whole information on its distribution. As a consequence, the statistical test about the mean of the fuzzified random variable can be considered in fact as a goodness-of-fit test for the original random variable and, analogously, the J J -sample test becomes a test for the equality of J J distributions. Comparative simulation studies of these procedures with respect to other well-known methods are carried out. A real-life example illustrates the introduced methodology.
goodness-of-fit fuzzy representation finite distributions equality of distributions hypothesis testing