Comparisons between largest order statistics from multiple-outlier models

In this work, we discuss stochastic comparisons between the largest order statistics from multiple-outlier models when the numbers of independent and identically distributed random variables are different. That is, if X-n:n(p,q) is the largest order statistic among X-1, ... , X-p, Xp+1, ... , X-n and X-n*:n* (p*,q*) is the largest order statistic among X-1, ... , X-p*, Xp*+1, ... , X-n*, where q = n - p and q* = n* - p*, we discuss whether X-n:n(p,q) and X-n*:n* (p*,q*) are ordered in some stochastic sense.