Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1149315 | Journal of Statistical Planning and Inference | 2010 | 11 Pages |
The statistical model is considered in which the collection of data from several independent populations is available only at random times determined by order statistics of lifetimes of a given number of objects. Each of the populations is distributed according to a general multiparameter exponential family. The problem is to estimate the mean value vector parameter of the multiparameter exponential family of distributions of the forthcoming observations. Under the loss function involving a weighted squared error loss, the cost proportional to the events appeared and a cost of observing the process, a class of optimal sequential procedures is established. The procedures are derived in two situations: when the lifetime distribution is completely known and in the case when it is unknown but assumed to belong to an exponential subfamily with an unknown failure rate parameter.