DNA methylation plays an important role in the development of many types of cancer. Identifying differentially methylated loci between cancer and normal patients is one of the central tasks to understand the contributions of the methylation process on cancer development. Through investigation of the methylation measurements generated by the Illumina methylation arrays, we notice that the methylation measurements of the cancer and normal groups could differ not only in means but also in variances. Therefore, we propose a generalized exponential tilt model to capture the differences in both means and variances between the cancer and normal groups. We derive the semiparametric tests to obtain model robustness. Through simulation studies, we demonstrate the feasibility of the proposed tests and a much improved power of the proposed tests than that of the t-test and the regression-based tests when the cancer and normal groups are different in variances only or in both means and variances. Hence the proposed tests can serve as useful complements to the standard tests that only test differences in means. We also illustrate the proposed methods by applying to a real methylation data from a recent study on ovarian cancer where the proposed methods identified additional methylation loci that were missed by the existing method.