In this letter, resource allocation is investigated for multiple pairs of secondary users in a cognitive underlay system. In the investigated system, the interference channel's statistics, including mean and variance, may change over time. It is assumed that a limit number of historical measurements of the interference channel's mean and variance are available. Based on the measurements, a minimum-volume elliptical region is used to describe the uncertainty of the interference channel's mean and variance. Sum capacity of multiple secondary users is maximized while limiting the worst-case interference outage probability. An optimization problem is formulated, which is non-convex. Global optimal solution is achieved by transforming the formulated non-convex problem into two level of convex optimization problems.