On the outstanding elements and record values in the exponential and gamma populations

Summary Outstanding elements and record values are discussed in this paper as related to exponential and gamma populations. First, the problem of prediction is considered when there are available,k sets of independent observations from a general-type exponential distribution. In such a case, prediction of then _k -th record value in thek-th set is made in terms ofn _i -th (i=1, …,k−1) record values from other (k−1) sets. For this purpose a predictive distribution is obtained. Secondly, the distribution of the sum of record values as well as that of a linear combination of record values are obtained for the exponential case. Probability integrals of the sum of record values and the probability integral of the sum of outstanding, elements are suggested for all values. Then, the distribution of then-th record values in a gamma population is put in a closed form. Further, the distribution of the linear combination of the spacings of outstanding elements as well as that of the linear combination of outstanding elements themselves are obtained. Finally the distribution of a ratio of two record values is obtained.