  We develop estimates for the equation of scalar curvature of singular metrics
with cone angle $\beta>1$, in a big and semi-positive cohomology class on a
K\"ahler manifold. We further derive the Laplacian estimate for the scalar
curvature equation of degenerate K\"ahler metrics. We then have several
applications of these estimates on the singular constant scalar curvature
K\"ahler metrics, which also include the singular K\"ahler-Einstein metrics.
