Invariant record processes and applications to best choice modelling
Let \(X_ 1,X_ 2,...,X_ n\) be a sequence of independent, identically distributed random variables. \(X_ j\) is said to be an r-record if \(X_ j\) is the r-th largest amongst \(X_ 1,...,X_ j\). Optimal selection based on relative ranks can be considered as a record problem. In fact, by considering the generating function of the number of r-records after index j and up to index n, all the classical results concerning the problem of maximizing the probability of choosing the best (highest) observation if only one selection is allowed, can be rederived simply and elegantly. This method can moreover be extended to include: - the problem of maximizing the probability of making the best selection if several choices are allowed; - the problem of maximizing a more complex reward function; - the case where the number n of observations is unknown, but is a random variable N with known distribution; - under certain conditions, the case where the number n of observations is unknown, and its distribution is also unknown.
maximizing the probability of choosing the best
scientific article; zbMATH DE number 4088636
scientific article