In principal-agent problem, the first-order approach is frequently used. To insure the validity of the approach the Monotone Likelihood Ratio Property and the Convexity of the Distribution Function Condition are requested. While the former property is satisfied by most of the distributions, this is not the case for the second property. We present two families of distributions for which the properties are satisfied. The first family includes as special cases the distributions that were previously introduced by various authors. The second family includes new distributions.