GENERALIZED MEAN OF ORDER $t$ VIA BOX AND COX'S TRANSFORMATION

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Published: Jun 1, 1994
DOI: https://doi.org/10.5556/j.tkjm.25.1994.4434
Keywords:
Mean of order $t$ Box and Cox's transformation probability distribution information-theoretic measures, unified (t,s)-mean

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VICENTE QUESADA
Departamento de Estadistica e 1.0 ., Facultad de Matema.ticas, Universidad Complutense de Madrid, 28.040-Madrid, Spain.
INDER JEET TANEJA
Departamento de Matema.tica, Universidade Federal de Santa Catarina, 88.049- Florian6polis, SC, Brazil.

Abstract




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.




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How to Cite
QUESADA, V., & TANEJA, I. J. (1994). GENERALIZED MEAN OF ORDER $t$ VIA BOX AND COX’S TRANSFORMATION. Tamkang Journal of Mathematics, 25(2), 125–141. https://doi.org/10.5556/j.tkjm.25.1994.4434
Issue
Vol. 25 No. 2 (1994)
Section
Papers
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