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interval_statistics [Tue Oct 26 06:43:01 2010] Alexander |
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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===== Relative Integrals Calculation ===== | ===== Relative Integrals Calculation ===== | ||
- | 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 | ^ Property | ||
- | | Integral | + | | //n// | The number of non-NaN (x,y) points |
- | | X Mean (expected value) | <m>mu = nu_1</m> | | + | | Y Sum (normalization) | <m>s = sum{j}{}{y_j}</m> | |
- | | Variance | + | | X Mean (first moment) |
- | | Standard deviation | < | + | | 2, 3, 4<sup>th</sup> [[wp> |
- | | Skewness | < | + | |
- | | Kurtosis | <m>gamma_2 = {mu_4} / {sigma^4} − 3</m> | | + | |
- | | Y Sum | < | + | |
- | Intermediate values are calculated as follows: | + | MagicPlot uses the following formulas to calculate intervals statistics: |
^ Property | ^ Property | ||
- | | [[wp>Raw moment|Raw moments]] | <m>nu_n = 1/s sum{k}{}{y_k {x_k}^n}, ~ n = 1...4, ~ s = sum{k}{}{y_k}</m> | | + | | Integral | Calculated using \\ [[integration|Trapezoidal rule]] | |
- | | [[wp> | + | | X Mean (expected value) |
+ | | Variance | < | ||
+ | | Standard deviation | ||
+ | | Skewness | <m>gamma_1 | ||
+ | | Kurtosis | <m>gamma_2 | ||
+ | ===== See Also ===== | ||
+ | * [[fitting]] | ||
+ | * [[spline]] | ||
+ | * [[statistics]] |