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Using a Generalized Mean as a Measure of Location
Author(s) -
Taylor Jeremy M. G.
Publication year - 1987
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710290611
Subject(s) - mathematics , skew , measure (data warehouse) , axiom , statistics , scale (ratio) , distribution (mathematics) , skewness , combinatorics , mathematical analysis , computer science , geometry , physics , telecommunications , database , quantum mechanics
In Taylor (1985 a) a measure of location, akin to a generalised mean was proposed, it's properties were studied for a particular family of skew distributions. The measure of location is essentially the retransformed mean after first transforming the observations to an approximately symmetric scale. Here it's properties are investigated for more general skew distributions. In particular, we study whether it satisfies the axioms for measures of location given in Bickel and Lehmann (1975). We show that it is estimating approximately the distribution median and through simulations we show that it is more efficient than the sample median.