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In this paper, we propose generalized fiducial methods and construct four generalized p-values to test the existence of quantitative trait locus effects under phenotype distributions from a location-scale family. Compared with the likelihood ratio test based on simulation studies, our methods perform better at controlling type I errors while retaining comparable power in cases with small or moderate sample sizes. The four generalized fiducial methods support varied scenarios: two of them are more aggressive and powerful, whereas the other two appear more conservative and robust. A real data example involving mouse blood pressure is used to illustrate our proposed methods.