Issues on discounting health effects have spurred debates on appropriate decision rules. Consensus is that empirically observed rates of time preference be incorporated in analysis. The latter, however, is known to suffer from cognitive limitations. The human nervous system perceives how long sensory events last and the latter impact on perceptual decision making which is the act of choosing from a set of alternatives on the basis of available sensory evidence; in our case the indifference balance between present and future consumption. Statistical tools for such purposes are however scarce and normality assumptions often fail to hold. We therefore derive a stochastic distribution by maximum entropy principle(MaxEnt). A MaxEnt distribution is one which best represents the current state of knowledge. Furthermore, MaxEnt distributions minimize the amount of prior information built into the distribution. Such distributions are usually sought by maximization of entropy constrained on what is known. In our case, we assume that the expected indifference amount at time t compared to an amount, y0, now is given by E(Y(t))=y0⁄w(t) where w(t) is a general time-inhomogeneous discount weight. With that constraint and the usual probability constraints, we  derive a maximum entropy distribution for such a future amount. That is, we provide a closed-form distribution of the probability that an individual is indifferent between some quantity Y(t)=y at time t and a quantity Y(0)=y0 now given E(Y(t))=y0/w(t).