A Statistical Estimator in a Problem of Stochastic Dominance

The assumed situation is as follows: two cumulative distribution functions F and G are in constant (unknown) ratio θ, for values of the random variables below t* (assumed known); F and G may behave entirely independently above t*. Observations on a sample from F are then used to obtain unbiased maximum likelihood estimates of and of other unknown parameters of G, denoted by λ. The estimators have application in problems of stochastic dominance in the context of portfolio analysis and in other situations of intertwining cumulative probability distributions.