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interval_statistics

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interval_statistics [Thu Jul 11 23:05:14 2013] Alexander |
interval_statistics [Mon Feb 17 16:12:02 2014] Alexander |
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Setting of intervals in ''Fit interval'' tab of Fit Plot was initially intended for specifying the range of data which are used for fitting by sum of fit curves. However, this tab can also be used to calculate integrals and statistics on these intervals (Statistics is only available in Pro edition). Data-Baseline is used to calculate the results. | Setting of intervals in ''Fit interval'' tab of Fit Plot was initially intended for specifying the range of data which are used for fitting by sum of fit curves. However, this tab can also be used to calculate integrals and statistics on these intervals (Statistics is only available in Pro edition). Data-Baseline is used to calculate the results. | ||

+ | ===== Peak Moments ===== | ||

MagicPlot can integrate data on selected intervals and calculate peak moments (x mean, variance, skewness, kurtosis). Spectrum line is treated as probability distribution curve: //x// values are treated as 'independent variable' and //y// values are treated as 'probability'. Standard statistical formulas are used to calculate moments (see below). | MagicPlot can integrate data on selected intervals and calculate peak moments (x mean, variance, skewness, kurtosis). Spectrum line is treated as probability distribution curve: //x// values are treated as 'independent variable' and //y// values are treated as 'probability'. Standard statistical formulas are used to calculate moments (see below). | ||

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^ Property ^ Formula ^ | ^ Property ^ Formula ^ | ||

| //n// | The number of non-NaN (x,y) points | | | //n// | The number of non-NaN (x,y) points | | ||

- | | X Mean | <m>nu_1 = 1/s sum{j}{}{y_j x_j}</m> | | + | | Y Sum (normalization) | <m>s = sum{j}{}{y_j}</m> | |

- | | [[wp>Central moment|Central moments]] | <m>mu_k = 1/s sum{j}{}{y_j (x_j − nu_1)^k}, ~ k = 2...4</m> | | + | | X Mean (first moment) | <m>nu_1 = 1/s sum{j}{}{y_j x_j}</m> | |

+ | | 2, 3, 4<sup>th</sup> [[wp>Central moment|Central moments]] | <m>mu_k = 1/s sum{j}{}{y_j (x_j − nu_1)^k}, ~ k = 2...4</m> | | ||

MagicPlot uses the following formulas to calculate intervals statistics: | MagicPlot uses the following formulas to calculate intervals statistics: | ||

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| Skewness | <m>gamma_1 = sqrt{n (n − 1)} / {n − 2} {mu_3} / {sigma^3}</m> | | | Skewness | <m>gamma_1 = sqrt{n (n − 1)} / {n − 2} {mu_3} / {sigma^3}</m> | | ||

| Kurtosis | <m>gamma_2 = {n − 1} / {(n − 2)(n − 3)} ({(n + 1) {mu_4} / {sigma^4} − 3 (n − 1)})</m> | | | Kurtosis | <m>gamma_2 = {n − 1} / {(n − 2)(n − 3)} ({(n + 1) {mu_4} / {sigma^4} − 3 (n − 1)})</m> | | ||

- | | Y Sum | <m>s = sum{j}{}{a_j}</m> | | ||

===== See Also ===== | ===== See Also ===== |

interval_statistics.txt · Last modified: Sun Nov 8 12:21:24 2015 (external edit)

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