Abstract-With the increasing importance of run-time leakage power dissipation (around 55% of total power), it has become necessary to accurately estimate it not only as a function of input vectors but also as a function of process parameters. Leakage power corresponding to the maximum vector presents itself as a higher bound for run-time leakage and is a measure of reliability. In this work, we address the problem of accurately estimating the probabilistic distribution of the maximum runtime leakage power in the presence of variations in process parameters such as threshold voltage, critical dimensions and doping concentration. Both sub-threshold and gate leakage current are considered. A heuristic approach is proposed to determine the vector that causes the maximum leakage power under the influence of random process variations. This vector is then used to estimate the lognormal distribution of the total leakage current of the circuit by summing up the lognormal leakage current distributions of the individual standard cells at their respective input levels. The proposed method has been effective in accurately estimating the leakage mean, standard deviation and probability density function (PDF) of ISCAS-85 benchmark circuits. The average errors of our method compared with near exhaustive random vector testing for mean and standard deviation are 1.32% and 1.41% respectively.