ON THE DISTRIBUTION OF THE MAXIMUM OF n INDEPENDENT NORMAL RANDOM VARIABLES: IID AND INID CASES

Abstract

The paper deals with the distribution of the maximum of n independent normal random variables and hints on some of its applications in the electricity power industry in the area of peak load estimation and in genetic selection for animal breeding. The paper provides for simple approximations to the mean of the largest order statistics both in the iid and non-identically distributed cases. Likewise, while the large sample results for the iid case have been treated in the past, we focused on the relatively unexplored non-identical but independent case. Large sample asymptotic results for extreme values of normal random variables are often used in reliability theory and also used in the analysis of extreme weather changes in relation to climate change. Results show that the large sample distribution for non-identically distributed case still obeys the Type I Gumbel distribution with shifted parameters through an application of Frechet’s stability postulate.