Open AccessGENERALIZED MEAN OF ORDER $t$ VIA BOX AND COX'S TRANSFORMATION
Author(s) -
Vicente Quesada,
Inder J. Taneja
Publication year - 1994
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.25.1994.4434
Subject(s) - mathematics , transformation (genetics) , kullback–leibler divergence , entropy (arrow of time) , divergence (linguistics) , order (exchange) , function (biology) , pure mathematics , combinatorics , statistics , biochemistry , chemistry , physics , linguistics , philosophy , finance , quantum mechanics , evolutionary biology , biology , economics , gene
Mean of order $t$ and Box and Cox's transformation function are very famous in the literature of mathematics and statistics respectively. In this paper, we have derived some standard inequalities from the mean of order $t$ and studied some interesting properties of Box and Cox's transformation function. A compos- iterelation of these two measures, calling generalized mean of order $t$ or unified $(t,s)$-mean is considered. The unified $(t,s)$-mean leads us to very important gen- eralized information theoretic measures. These measures include generalizations of Shannon's entropy, Kullback-leibler's relative information, Kerridge's inaccu- racy, J-divergence, Jensen difference dive~gence measure, etc. Properties of unified $(t,s)$-mean are also studied.