Difference between revisions of "CumNormal"
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Returns the cumulative probability | Returns the cumulative probability | ||
:<math>p = Pr[x \le X] = {1\over{\sigma \sqrt{2\pi}}} \int_{-\infty}^x exp\left(- {1\over 2} {{(X-\mu)^2}\over\sigma^2}\right)</math> | :<math>p = Pr[x \le X] = {1\over{\sigma \sqrt{2\pi}}} \int_{-\infty}^x exp\left(- {1\over 2} {{(X-\mu)^2}\over\sigma^2}\right)</math> | ||
| − | for a [[Normal|normal distribution]] with a given mean and standard deviation. | + | for a [[Normal|normal distribution]] with a given mean and standard deviation. «Mean» and «stddev» are optional and default to ''Mean = 0'', ''stddev = 1''. |
:<code>CumNormal(1) - CumNormal( -1 )</code> → .683 | :<code>CumNormal(1) - CumNormal( -1 )</code> → .683 | ||
i.e., 68.3% of the area under a normal distribution is contained | i.e., 68.3% of the area under a normal distribution is contained | ||
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[[image:CumNormalGraph.png]] | [[image:CumNormalGraph.png]] | ||
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= See Also = | = See Also = | ||
Revision as of 16:42, 21 August 2015
CumNormal(X,mean,stddev)
Returns the cumulative probability
- [math]\displaystyle{ p = Pr[x \le X] = {1\over{\sigma \sqrt{2\pi}}} \int_{-\infty}^x exp\left(- {1\over 2} {{(X-\mu)^2}\over\sigma^2}\right) }[/math]
for a normal distribution with a given mean and standard deviation. «Mean» and «stddev» are optional and default to Mean = 0, stddev = 1.
CumNormal(1) - CumNormal( -1 )→ .683
i.e., 68.3% of the area under a normal distribution is contained within one standard deviation of the mean.
See Also
- CumNormalInv -- the inverse cumulative density
- Normal -- The normal distribution
- Erf -- The closely related error function
- Sigmoid(x) -- Another sigmoidal-shaped function
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