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 Xn:n(p,q) is the largest order statistic among X1,…,Xp,Xp+1,…,Xn and Xn∗:n∗(p∗,q∗) is the largest order statistic among X1,…,Xp∗,Xp∗+1,…,Xn∗, where q=n−p and q∗=n∗−p∗, we discuss whether Xn:n(p,q) and Xn∗:n∗(p∗,q∗) are ordered in some stochastic sense.