Dr. John Kolassa
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The relationship between the first few moments and cumulants, | The relationship between the first few moments and cumulants, | ||
obtained by extracting coefficients from the expansion, is as follows | obtained by extracting coefficients from the expansion, is as follows | ||
| − | :<math forward> | + | :<math forward>\begin{array}{lcr} |
\kappa_1 &=& \mu_1\nonumber \\ | \kappa_1 &=& \mu_1\nonumber \\ | ||
\kappa_2 &=& \mu_2 - \mu_1^2\nonumber\\ | \kappa_2 &=& \mu_2 - \mu_1^2\nonumber\\ | ||
| Line 63: | Line 63: | ||
</math> | </math> | ||
In the reverse direction | In the reverse direction | ||
| − | :<math reverse> | + | :<math reverse>\begin{array}{lcr} |
\mu_2 &=& \kappa_2 + \kappa_1^2\nonumber\\ | \mu_2 &=& \kappa_2 + \kappa_1^2\nonumber\\ | ||
\mu_3 &=& \kappa_3 + 3\kappa_2\kappa_1 + \kappa_1^3\\ | \mu_3 &=& \kappa_3 + 3\kappa_2\kappa_1 + \kappa_1^3\\ | ||
