Bounds on the mean of the maximum of a number of normal random variables

Abstract

A simple method producing lower and upper bounds on E max(X₁,...,X_n) is presented under assumption that the X_i's are independent normal random variables. Furthermore the upper bounds are determined when the X_i's are normal and positively correlated

Keywords:

• Multivariate normal distribution
• convex order relation
• maximum
• expected value
• bounds