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

Many times, aspects of populations exist that must satisfy a stochastic ordering requirement. Nevertheless, estimates may not bear out this stochastic ordering because of the inherent variability of the observations. This article will consider the problem of finding maximum likelihood estimates of stochastically ordered survival functions for the cases (a) one survival function being fixed in advance and (b) estimating two survival functions when the data include censored observations. A numerical example is discussed in detail to illustrate the solution to this problem.