Ordering properties of the second smallest and the second largest order statistics from a general semiparametric family of distributions

In this article, we consider the second smallest and the second largest order statistics from a general semiparametric family of distributions. The fail-safe system, the second-price sealed-bid auction, the second-price reversed auction are some classic examples where these order statistics are used. Here, we derive some stochastic comparisons results for these order statistics. Further, we show that the developed results hold for many well-known semiparametric models, namely, proportional hazard and reversed rates models, scale model, and proportional odds model.