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A statistical method widely used to test the hypothesis of equality of two survival functions (S1 and S2 within the same family of parametric probability distributions) is the likelihood ratio (LR) whose asymptotic distribution under the hypothesis H0: S1 = S2 and under regular conditions is a Chi-square distribution. We conducted a study by simulating LR statistical distribution under H0 when the data come from a Weibull distribution subject to random censorship. The objective was to assess whether or not the asymptotic results, valid for the LR statistical distribution in the case of Weibull distribution, are also valid in the presence of censorship. It was observed that as the sample size increases, the approximation by a chi-square distribution X2(2) shows adequate for empirical statistical distribution of LR, even in the presence of censure.
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