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Microbending loss formula is derived for arbitrary-index profile optical fibers by using analytical curved fiber fields to the first-order perturbation theory. Relation between loss and fiber curvature power spectral statistics is studied in detail. Normalized frequency giving the minimum microbending loss value scarcely depends on the power spectrum. The larger the propagation constant difference between the guided and quasi-guided modes, the smaller the microbending loss is in regard to wavelength, relative index difference, and normalized frequency dependence. The obtained formulas for single-mode fiber show the same dependence as the graded-index multimode fiber, with respect to fiber structure and curvature statistical parameters.