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interval_statistics [Fri Nov 5 13:58:11 2010] Gray |
interval_statistics [Thu Jan 14 17:19:58 2021] (current) Alexander |
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====== Calculating Integrals and Statistics on Intervals using Fit Plot ====== | ====== Calculating Integrals and Statistics on Intervals using Fit Plot ====== | ||
- | Setting intervals in '' | ||
- | MagicPlot can integrate data on selected | + | Setting of intervals |
- | Statistical data and integrals are automatically updated if //x// or //y// data is changed or intervals are changed. | + | ===== 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 ' | ||
+ | |||
+ | Statistical data and integrals are automatically updated if //x// or //y// data are changed or intervals are changed. | ||
{{: | {{: | ||
- | All statistical data is summarized in the intervals table: | + | All statistical data are summarized in the intervals table: |
- | {{: | + | {{: |
===== Managing Intervals ===== | ===== Managing Intervals ===== | ||
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MagicPlot can calculate relative integrals to compare the relative intensity of spectrum lines. To compute relative integrals set '' | MagicPlot can calculate relative integrals to compare the relative intensity of spectrum lines. To compute relative integrals set '' | ||
- | ===== Formulas ===== | + | ===== Computational |
+ | Central moments are calculated as follows (see table). All sums are calculated using [[wp> | ||
+ | ^ Property | ||
+ | | //n// | The number of non-NaN (x,y) points | ||
+ | | Y Sum (normalization) | <m>s = sum{j}{}{y_j}</ | ||
+ | | X Mean (first moment) | < | ||
+ | | 2, 3, 4< | ||
MagicPlot uses the following formulas to calculate intervals statistics: | MagicPlot uses the following formulas to calculate intervals statistics: | ||
^ Property | ^ Property | ||
| Integral | Calculated using \\ [[integration|Trapezoidal rule]] | | | Integral | Calculated using \\ [[integration|Trapezoidal rule]] | | ||
| X Mean (expected value) | <m>mu = nu_1</ | | X Mean (expected value) | <m>mu = nu_1</ | ||
- | | Variance | < | + | | Variance | < |
- | | Standard deviation | < | + | | Standard deviation | < |
- | | Skewness | < | + | | Skewness | < |
- | | Kurtosis | < | + | | Kurtosis | < |
- | | Y Sum | <m>s = sum{k}{}{y_k}</m> | | + | |
- | + | ||
- | Intermediate values are calculated as follows: | + | |
- | ^ Property | + | |
- | | [[wp>Raw moment|Raw moments]] | < | + | |
- | | [[wp> | + | |
===== See Also ===== | ===== See Also ===== | ||
* [[fitting]] | * [[fitting]] | ||
* [[spline]] | * [[spline]] | ||
+ | * [[statistics]] |