Duration problem: basic concept and some extensions

Zdzisław Porosiński, Marek Skarupski, and Krzysztof Szajowski. "Duration problem: basic concept and some extensions." Mathematica Applicanda 44.1 (2016): null. <http://eudml.org/doc/293086>.

@article{ZdzisławPorosiński2016,
abstract = {  We consider a sequence of independent random variables with the known distribution observed sequentially. The observation n is a value of one order statistics s : n-th, where 1 ≤ s ≤ n. It the instances following the n-th observation it may remain of the s : m or it will be the value of the order statistics r : m (of m > n observations). Changing the rank of the observation, along with expanding a set of observations is a random phenomenon that is difficult to predict. From practical reasons it is of great interest. Among others, we pose the question of the moment in which the observation appears and whose rank will not change significantly until the end of sampling of a certain size. We also attempt to answer which observation should be kept to have the "good quality observation" as long as possible. This last question was analysed by Ferguson, Hardwick and Tamaki (1991) in the abstract form which they called the problem of duration.This article gives a systematical presentation of known duration models and some new generalization. We collect results from different papers on the duration of the extremal observation in the no-information (say rank based) case and the full-information case. In the case of non-extremal observation duration models the most appealing are various setting related to the two extremal order statistic. In the no-information case it will be the maximizing duration of owning the relatively the best or the second best object. The idea was formulated and the problem was solved by Szajowski and Tamaki (2006). The full-information duration problem with special requirement was presented by Kurushima and Ano (2010).},
author = {Zdzisław Porosiński, Marek Skarupski, Krzysztof Szajowski},
journal = {Mathematica Applicanda},
keywords = {optimal stopping; duration problem; secretary problem},
language = {eng},
number = {1},
pages = {null},
title = {Duration problem: basic concept and some extensions},
url = {http://eudml.org/doc/293086},
volume = {44},
year = {2016},
}

TY - JOUR
AU - Zdzisław Porosiński
AU - Marek Skarupski
AU - Krzysztof Szajowski
TI - Duration problem: basic concept and some extensions
JO - Mathematica Applicanda
PY - 2016
VL - 44
IS - 1
SP - null
AB -   We consider a sequence of independent random variables with the known distribution observed sequentially. The observation n is a value of one order statistics s : n-th, where 1 ≤ s ≤ n. It the instances following the n-th observation it may remain of the s : m or it will be the value of the order statistics r : m (of m > n observations). Changing the rank of the observation, along with expanding a set of observations is a random phenomenon that is difficult to predict. From practical reasons it is of great interest. Among others, we pose the question of the moment in which the observation appears and whose rank will not change significantly until the end of sampling of a certain size. We also attempt to answer which observation should be kept to have the "good quality observation" as long as possible. This last question was analysed by Ferguson, Hardwick and Tamaki (1991) in the abstract form which they called the problem of duration.This article gives a systematical presentation of known duration models and some new generalization. We collect results from different papers on the duration of the extremal observation in the no-information (say rank based) case and the full-information case. In the case of non-extremal observation duration models the most appealing are various setting related to the two extremal order statistic. In the no-information case it will be the maximizing duration of owning the relatively the best or the second best object. The idea was formulated and the problem was solved by Szajowski and Tamaki (2006). The full-information duration problem with special requirement was presented by Kurushima and Ano (2010).
LA - eng
KW - optimal stopping; duration problem; secretary problem
UR - http://eudml.org/doc/293086
ER -