Interested Article - Индекс Тейла

?????? ????? ???????????? ????? ?????????? ????????? ??????????? ???????????, ???????????? ? 1967 ???? ????????????? ??????????? ???? ?????? . ?????? ????? ??????? ?? ???????????? ???????? ??????? ?????????????? ???????? . ? ??????? ?? ???????????? ????? ?????? ????? ????????, ?? ????, ???? ????????? ??????? ?? ??????, ?? ?????? ????? ???? ????????? ????? ???????? ? ???? ?????????? ????? ???????? ????? ?????? ?? ????? ? ?????????? ??????????? ??????????? ????? ????????. ???????????? ??????? ????? ????????? ???????? ? ???????? ??????????? ???????????, ??????????? ???????? ?????????? ????????? ?? ??????, ? ?????????? ????????? ????????? .

?????? ??????? ?????

??????? ????? $T_{1}$ ? $T_{0}$ ?????????????? ?? ????????? ???????? :

T_{1}={\frac {1}{N}}\sum _{i=1}^{N}\left({\frac {x_{i}}{\overline {x}}}\cdot \ln {\frac {x_{i}}{\overline {x}}}\right)

T_{0}={\frac {1}{N}}\sum _{i=1}^{N}\left(\ln {\frac {\overline {x}}{x_{i}}}\right)

??? $x_{i}$ ????? $i$ -?? ???????????, ${\overline {x}}={\frac {1}{N}}\sum _{i=1}^{N}x_{i}$ ??????? ???????? ??????, ? $N$ ?????????? ???????????? ? ?????????. ???? ?????? ???? ???????????? ?????, ?? ??????? ????? ????? ????. ???? ????? ???? ????????? ??????????????? ? ????? ?????? ???????????, ?? ??????? ????? ????? ln N . ?????? ? ?????????? ???????? ????? ?????????? ?????? ?????? $T_{1}$ , ? ?? ????? ??? $T_{0}$ ?????????? ????????????????????? ??????????? . ????????????????????? ?????????? ????????????? ? ?????????? ? ?????? ??????? ????? ?????????????, ? ?? ????? ??? ?????? ????? ????????? ???????????? ? ?????????? ?? ???? ????? ????????????? .

???????????? ??????? ?????

???? ????????? ??????? ?? ?????? $G_{1},...,G_{J}$ , ?? ?????? ????? ????? ???????? ???

T=\sum _{j=1}^{J}\omega _{j}*T(G_{j})+T(\{y_{1},...,y_{J}\}),

??? $\omega _{j}={\frac {N_{j}}{N}}{\frac {y_{j}}{\overline {x}}}$ , $y_{j}$ — ??????? ???????? ?????? ? ?????? $G_{j}$ , ${\overline {x}}={\frac {1}{N}}\sum _{i=1}^{N}x_{i}$ ??????? ???????? ?????? ?? ???? ?????????, $N_{j}$ — ?????????? ???????????? ? ?????? $G_{j}$ ? $N$ — ?????????? ???????????? ? ????????? . ????????? ${\frac {T(\{y_{1},...,y_{J}\})}{T}}$ — ??????? ??????????? ???????????, ?????????? ???????? ?????????? ?? ??????. ???, ?? 32,6 % ??????????? ??????? ???????? ? ????????? ????? ???? ????????? ??????? ??????????? ????? ?????, 18,9 % ?????????? ?????????? ? ?????? 2,6 % ???????? ????? ????? .

?????????????? ??????????? ??????? ?????

?????? ????? ??????????? ?? ????????? ? ?????????, ?? ????, ?? ?? ?????????? ??? ???????????. ?????? ????? ?? ??????????? ?? ????????? ? ????????.

?????? ????? ? ?????? ?????????

?????? ????????? ??????????? ? ??????????? ??????? $1-e^{-T}$ , ??? $T$ — ?????? ????? .

?????????? ??????? ?????

????? ?????????????? ?????????? ? ??????? ????????? , ?????? ????? ???????????? ??? ?????? ???????? ????????????? ?????? ? ????????????? ?????? ???????????? ??????????? .

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?????????????? ??????? ????????? ?????????? ??????? ????? ? ??????? ?????? «ineq».
??????????? ????? ???????? ? ??? ??????? .

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. ???? ?????????: 19 ??????? 2010. ???????????? ?? 25 ????? 2009 ????.
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. ???? ?????????: 19 ??????? 2010. 5 ?????? 2010 ????.
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