Difference between revisions of "File:2014.12.26rubleDollar.png"

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Price of 100 ruddian rubles, measured in the USA cents; data for the end of year 2014
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and the approximations with elementary functions.
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  +
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The green thick curve represents the experimental data
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$y=g(x)=\mathrm{Measured}(x)$
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by https://www.mataf.net/en/currency/converter-USD-RUB ;
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coordinate $x$ has sense of time, measured in days since the date of beginning of the project,
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2014,10,27.
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For each datum stored for specified year,month,day, the time $x$ is evaluated as
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$x = \rm
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daju24(year,month, day)-
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daju24(2014,10, 27)$
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with function daju24 defined below in C++: \begin{verbatim}
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<poem>
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int daju24(int Y,int M, int D){ int a, y, m;
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a = (14-M)/12;
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y = Y + 4800 - a;
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m = M + 12*a - 3;
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return D + (153*m+2)/5 + 365*y + y/4 - y/100 + y/400 - 32045 - 2400000; }
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</poem>
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These data are stored as array $\{x_n,g_n\}, \{n,1,M\}$,
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where $M$ is total number of experimental data. Approximating functions are specified below:
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$
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\begin{array}{c|l|r|r}
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\rm Label &~ ~ ~ ~ ~ f(x) & D ~ ~ & Q ~ ~\\
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\hline
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\rm Linear &227.323 - 0.583872 x &\! 10.52733 &\! 13.15973\\
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%{227.32289289657714` - 0.5838719175561293` x, 10.52725166548383`, 13.15967254961913`}
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\rm Qu\! & 233.214 - 0.908933 x - 0.00361841 x^2 & 3.94609& 5.84960\\
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%3.946087936982961`, 5.849600340588587
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\rm Ellipse &~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1.19332 \sqrt{(99.8879 - x) (388.557 + x)} & 3.72305 & 5.74477\\
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\rm Ed & -96.8595 + 1.46555 \sqrt{(127.305 - x) (401.761 + x)} & 3.74359 & 5.71801\\
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\rm Cu & 234.636 - 0.905604 x - 0.00456087 x^2 - 6.98113\!\times\!10^{-6}~ x^3 & 3.77297 & 5.72430\\
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\rm Bell & 291.207 / \cosh(0.715005 + 0.00630878 x)& 4.91540& 6.96990\\
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\rm Gauss & 290.656 \exp\Big(-0.0000168642 (116.58 + x)^2\Big) & 4.45347&6.43202\\
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\rm Dex &\!\! 100/\Big(0.337261 \exp(0.000020293 x) + 0.0881639 \exp(0.0189706 x)\Big) \!& 3.79927& 5.72350\\
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\hline
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\end{array}
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$
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The last two columns of the table above characterise the precision of each approximation:
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$\displaystyle D= \frac{1}{M} \sum_{n=1}^{M} |f(x_n)-g_n|$
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$\displaystyle Q= \sqrt{\frac{1}{M} \sum_{n=1}^{M} (f(x_n)-g_n)^2}$
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These quantities refer to date 2014.12.26; $M=209$.
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==Refrerences==
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<references/>
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http://mizugadro.mydns.jp/PAPERS/2015ruble.pdf
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D.Kouznetsov. Fitting of economical data with elementary functions: rouble versus dollar in 2014.
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[[Category:Approximation of rubble]]
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[[Category:Ruble]]
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[[Category:Rouble]]
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[[Category:Inflation]]
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[[Category:Russia]]
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[[Category:Corruption]]
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[[Category:Implicit plot]]

Latest revision as of 08:26, 1 December 2018

Price of 100 ruddian rubles, measured in the USA cents; data for the end of year 2014 and the approximations with elementary functions.


The green thick curve represents the experimental data $y=g(x)=\mathrm{Measured}(x)$ by https://www.mataf.net/en/currency/converter-USD-RUB ; coordinate $x$ has sense of time, measured in days since the date of beginning of the project, 2014,10,27.

For each datum stored for specified year,month,day, the time $x$ is evaluated as

$x = \rm daju24(year,month, day)- daju24(2014,10, 27)$

with function daju24 defined below in C++: \begin{verbatim} '"`UNIQ--poem-00000000-QINU`"' These data are stored as array $\{x_n,g_n\}, \{n,1,M\}$, where $M$ is total number of experimental data. Approximating functions are specified below: $ \begin{array}{c|l|r|r} \rm Label &~ ~ ~ ~ ~ f(x) & D ~ ~ & Q ~ ~\\ \hline \rm Linear &227.323 - 0.583872 x &\! 10.52733 &\! 13.15973\\ %{227.32289289657714` - 0.5838719175561293` x, 10.52725166548383`, 13.15967254961913`} \rm Qu\! & 233.214 - 0.908933 x - 0.00361841 x^2 & 3.94609& 5.84960\\ %3.946087936982961`, 5.849600340588587 \rm Ellipse &~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1.19332 \sqrt{(99.8879 - x) (388.557 + x)} & 3.72305 & 5.74477\\ \rm Ed & -96.8595 + 1.46555 \sqrt{(127.305 - x) (401.761 + x)} & 3.74359 & 5.71801\\ \rm Cu & 234.636 - 0.905604 x - 0.00456087 x^2 - 6.98113\!\times\!10^{-6}~ x^3 & 3.77297 & 5.72430\\ \rm Bell & 291.207 / \cosh(0.715005 + 0.00630878 x)& 4.91540& 6.96990\\ \rm Gauss & 290.656 \exp\Big(-0.0000168642 (116.58 + x)^2\Big) & 4.45347&6.43202\\ \rm Dex &\!\! 100/\Big(0.337261 \exp(0.000020293 x) + 0.0881639 \exp(0.0189706 x)\Big) \!& 3.79927& 5.72350\\ \hline \end{array} $

The last two columns of the table above characterise the precision of each approximation:

$\displaystyle D= \frac{1}{M} \sum_{n=1}^{M} |f(x_n)-g_n|$

$\displaystyle Q= \sqrt{\frac{1}{M} \sum_{n=1}^{M} (f(x_n)-g_n)^2}$

These quantities refer to date 2014.12.26; $M=209$.

Refrerences


http://mizugadro.mydns.jp/PAPERS/2015ruble.pdf D.Kouznetsov. Fitting of economical data with elementary functions: rouble versus dollar in 2014.

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