GMS:Risk Analysis Wizard: Difference between revisions
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<!--[[Image:wt_eq.gif]] | <!--[[Image:wt_eq.gif]] | ||
<math>{\displaystyle w_i = \alpha ^ {\left [ \frac{ME-E_i}{SD} \right ]}}</math>--> | <math>{\displaystyle w_i = \alpha ^ {\left [ \frac{ME-E_i}{SD} \right ]}}</math>--> | ||
[[Image:riskwizardeq1.jpg]] ......................(1) | ::[[Image:riskwizardeq1.jpg]] ......................(1) | ||
:Where W<sub>i</sub> is the weight applied to solution i, [[Image:alpha_char.gif]] is a user-defined factor, ME is the mean of the error values from all solutions, E<sub>jk</sub> is the error for solution i, and SD is the standard deviation of error values from all solutions. The weights are also normalized as follows | :Where W<sub>i</sub> is the weight applied to solution i, [[Image:alpha_char.gif]] is a user-defined factor, ME is the mean of the error values from all solutions, E<sub>jk</sub> is the error for solution i, and SD is the standard deviation of error values from all solutions. The weights are also normalized as follows | ||
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<!--[[Image:wt_final.gif]] | <!--[[Image:wt_final.gif]] | ||
<math>{\displaystyle w_{final} = \frac{w_i}{\sum w_i}}</math>--> | <math>{\displaystyle w_{final} = \frac{w_i}{\sum w_i}}</math>--> | ||
[[Image:riskwizardeq2.jpg]] .......................(2) | ::[[Image:riskwizardeq2.jpg]] .......................(2) | ||
:so that the weights sum to unity. Equation 1 was developed to give the greater emphasis to the lower error values and to allow the user to control the relative emphasis given to low vs. high values simply by adjusting the [[Image:alpha_char.gif]] value. The equation also avoids problems when one of the error values is zero, since a zero error value does not result in an infinite weight. We also wanted the equation to scale the weights according to the data being examined. This is done by subtracting the individual SSWR from the mean error and dividing by the standard deviation. | :so that the weights sum to unity. Equation 1 was developed to give the greater emphasis to the lower error values and to allow the user to control the relative emphasis given to low vs. high values simply by adjusting the [[Image:alpha_char.gif]] value. The equation also avoids problems when one of the error values is zero, since a zero error value does not result in an infinite weight. We also wanted the equation to scale the weights according to the data being examined. This is done by subtracting the individual SSWR from the mean error and dividing by the standard deviation. | ||
