Some more results on a generalized `useful' R-norm information measure
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Abstract
A parametric mean length is defined as the quantity
$$ _{R\beta} L_u = \frac{R}{R-1} \Bigg [1 - \sum P_i^\beta \bigg (\frac{u_i}{ \sum u_ip_i^\beta}\bigg )^{\frac{1}{R}} D^{-n_i \Big (\frac{R-1}{R}\Big )}\Bigg ], $$
where $R>0$ ($\not=1$), $\sum p_i=1$. This being the useful mean length of code words weighted by utilities, $u_i$. Lower and upper bounds for $_{R\beta} L_u$ are derived in terms of `useful'-R-norm information measure for the incomplete power distribution, $p^\beta$.
$$ _{R\beta} L_u = \frac{R}{R-1} \Bigg [1 - \sum P_i^\beta \bigg (\frac{u_i}{ \sum u_ip_i^\beta}\bigg )^{\frac{1}{R}} D^{-n_i \Big (\frac{R-1}{R}\Big )}\Bigg ], $$
where $R>0$ ($\not=1$), $\sum p_i=1$. This being the useful mean length of code words weighted by utilities, $u_i$. Lower and upper bounds for $_{R\beta} L_u$ are derived in terms of `useful'-R-norm information measure for the incomplete power distribution, $p^\beta$.
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How to Cite
Kumar, S. (2009). Some more results on a generalized `useful’ R-norm information measure. Tamkang Journal of Mathematics, 40(2), 211–216. https://doi.org/10.5556/j.tkjm.40.2009.469
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