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lib/node_modules/@stdlib/stats/incr Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -43,13 +43,13 @@ Using a univariate normal distribution as the standard of comparison, the [exces
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4444For a sample of ` n ` values, the [ sample excess kurtosis] [ sample-excess-kurtosis ] is
4545
46- <!-- <equation class="equation" label="eq:sample_excess_kurtosis" align="center" raw="g_2 = \frac{m_4}{m_2^2} - 3 = \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2}" alt="Equation for the sample excess kurtosis."> -->
46+ <!-- <equation class="equation" label="eq:sample_excess_kurtosis" align="center" raw="g_2 = \frac{m_4}{m_2^2} - 3 = \frac{\frac{1}{n} \displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\frac{1}{n} \displaystyle \sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2}" alt="Equation for the sample excess kurtosis."> -->
4747
4848``` math
49- g_2 = \frac{m_4}{m_2^2} - 3 = \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2}
49+ g_2 = \frac{m_4}{m_2^2} - 3 = \frac{\frac{1}{n} \displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\frac{1}{n} \displaystyle \sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2}
5050```
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52- <!-- <div class="equation" align="center" data-raw-text="g_2 = \frac{m_4}{m_2^2} - 3 = \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2}" data-equation="eq:sample_excess_kurtosis">
52+ <!-- <div class="equation" align="center" data-raw-text="g_2 = \frac{m_4}{m_2^2} - 3 = \frac{\frac{1}{n} \displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\frac{1}{n} \displaystyle \sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2}" data-equation="eq:sample_excess_kurtosis">
5353 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/kurtosis/docs/img/equation_sample_excess_kurtosis.svg" alt="Equation for the sample excess kurtosis.">
5454 <br>
5555</div> -->
Original file line number Diff line number Diff line change @@ -43,13 +43,13 @@ where the numerator is the [covariance][covariance] and the denominator is the p
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4444For a sample of size ` W ` , the [ sample Pearson product-moment correlation coefficient] [ pearson-correlation ] is defined as
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46- <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
46+ <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\ sqrt{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})^2} \displaystyle\ sqrt{\displaystyle \sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
4747
4848``` math
49- r = \frac{\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
49+ r = \frac{\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})^2} \displaystyle\ sqrt{\displaystyle \sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
5050```
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52- <!-- <div class="equation" align="center" data-raw-text="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
52+ <!-- <div class="equation" align="center" data-raw-text="r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\ sqrt{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})^2} \displaystyle\ sqrt{\displaystyle \sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
5353 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/mpcorr/docs/img/equation_sample_pearson_correlation_coefficient.svg" alt="Equation for the sample Pearson product-moment correlation coefficient.">
5454 <br>
5555</div> -->
Original file line number Diff line number Diff line change @@ -43,13 +43,13 @@ where the numerator is the [covariance][covariance] and the denominator is the p
4343
4444For a sample of size ` W ` , the sample [ Pearson product-moment correlation coefficient] [ pearson-correlation ] is defined as
4545
46- <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
46+ <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\ sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \displaystyle\ sqrt{\displaystyle \sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
4747
4848``` math
49- r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
49+ r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\ sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \displaystyle\ sqrt{\displaystyle \sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
5050```
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52- <!-- <div class="equation" align="center" data-raw-text="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
52+ <!-- <div class="equation" align="center" data-raw-text="r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\ sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \displaystyle\ sqrt{\displaystyle \sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
5353 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@e6bc812ab63010afd0f25418c0c6954c3a680357/lib/node_modules/@stdlib/stats/incr/mpcorr2/docs/img/equation_sample_pearson_correlation_coefficient.svg" alt="Equation for the sample Pearson product-moment correlation coefficient.">
5454 <br>
5555</div> -->
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