Distribution of the Maximum of the Arithmetic Mean of Correlated Random Variables

Abstract

The initial distribution considered here is obtained from a multivariate analogue of the Pearson Type III distribution, and the value of the correlation is taken to be non-negative. There is obtained here the distribution of the maximum in samples of fixed size $n$ from a random variable which is the arithmetic mean of $k$ such correlated random variables. This distribution is obtained for large values of $n$ and for large values of $k$. The appropriate expressions for the mode and scale parameters are also given.