Some Investigations of the Sample Maximum

Wolfgang Gohout () and Katja Specht ()
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Wolfgang Gohout: Hochschule Pforzheim, Tiefenbronner Str. 65, D–75175 Pforzheim, Germany
Katja Specht: Technische Hochschule Mittelhessen, Wilhelm–Leuschner–Str. 13, D–61169 Friedberg, Germany

Interdisciplinary Management Research, 2015, vol. 11, 1173-1186

Abstract: Day by day we are confronted with records and extremes. Newsletters and media report on the hottest day, the highest tide, the best–performing investment fund, and so on. And often people wonder at the level of these extreme values. The sheer amount of the maximum income or property of the richest one out of some millions of people easily contradicts human intuition and may lead to envy and jealousy. In this paper, we consider some examples and various methods of estimating the sample maximum. Starting with a simple introductory example, we are going to raise the difficulty as well as the realism of our exemplary applications. The multivariate normal case may be treated by simulation and will be illustrated with annual yields of some DAX30 equities. The asymptotic estimation is well established. A proper example is the private wealth of the richest Germans, which has been investigated by a special issue of the social–economic panel study (SOEP) by DIW. It will be shown that the amount of wealth of the richest German is not so surprising.

Date: 2015
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