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The identric mean of two positive real numbers x, y is defined as:[1]
It can be derived from the mean value theorem by considering the secant of the graph of the function . It can be generalized to more variables according by the mean value theorem for divided differences. The identric mean is a special case of the Stolarsky mean.
^RICHARDS, KENDALL C; HILARI C. TIEDEMAN (2006). "A NOTE ON WEIGHTED IDENTRIC AND LOGARITHMIC MEANS" (PDF). Journal of Inequalities in Pure and Applied Mathematics. 7 (5). Archived (PDF) from the original on 21 September 2013. Retrieved 20 September 2013.
The identricmean of two positive real numbers x, y is defined as: I ( x , y ) = 1 e ⋅ lim ( ξ , η ) → ( x , y ) ξ ξ η η ξ − η = lim ( ξ , η ) → ( x ...
Heronian meanIdentricmean Lehmer mean Logarithmic mean Moving average Neuman–Sándor mean Quasi-arithmetic mean Root mean square (quadratic mean) Rényi's...
power mean with exponent 1 2 {\displaystyle {\frac {1}{2}}} . lim p → 1 S p ( x , y ) {\displaystyle \lim _{p\to 1}S_{p}(x,y)} is the identricmean. It...
misrepresentation. This family includes the logarithmic mean, geometric mean, and the identricmean. The Stolarsky means can be justified as minimizing these...