The electricity price duration curve (EPDC) represents the probability distribution function of the electricity price considered as a random variable. The price uncertainty comes both from the demand side and the supply side, since the load varies continuously, and not all generators may be available at all times. The production costs of electricity also fluctuate with the price of fuel. EPDCs have many application including the valuation of incremental generation assets or forward contracts on the energy produced by such assets, estimating capacity cost recovery and valuation of energy call options. Traditional approaches for calculating EPDCs were based on approximation methods such as the method of cumulants using Edgeworth expansions of multivariate probability distributions. This paper presents a new approach to compute numerically the EPDC under price and quantity competition models. This numerical method provide both exact numerical results and modeling flexibility. It is based on inference algorithms in probabilistic graphical models (PGMs) which exploit conditional independence relationships among the random variables.