Maximum Likelihood Estimation of the Survival Functions of Stochastically Ordered Random Variables

摘要

Many times populations exist which logically must satisfy a stochastic ordering requirement. Nevertheless, estimates of these populations may not bear out this stochastic ordering because of the inherent variability of the observations. This paper will consider the problem of finding maximum likelihood estimates of stochastically ordered survival functions for the cases (a) one survival being fixed in advance and (b) estimating both survival functions when the data includes censored observations. A numerical example is handled in detail to illustrate the solution to this problem. (Author)