Permanent Expressions for Order Statistic Densities

Summary Of late there has been a need to extend the traditional concept of an order statistic. Either the ordered statistics are obtained from statistics which are assumed to be correlated but with identical marginal densities (Young, 1967; Takahasi, 1969) or they are obtained from statistics which are sampled independently from different populations (Loynes, 1966; Tong, 1970). This note demonstrates that the marginal densities of the order statistics obtained by the latter extension can be expressed neatly by the use of permanents. The results appear to be new and one of the authors (Vaughan, 1970) has used these results in traffic research.