Difference between revisions of "CumNormal"
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| − | = CumNormal(X, mean, stddev) = | + | == CumNormal(X, mean, stddev) == |
| + | Returns the cumulative probability | ||
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:<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. «Mean» and «stddev» are optional and default to ''Mean = 0'', ''stddev = 1''. | for a [[Normal|normal distribution]] with a given mean and standard deviation. «Mean» and «stddev» are optional and default to ''Mean = 0'', ''stddev = 1''. | ||
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| − | + | :<code>CumNormal(1) - CumNormal(-1) → .683</code> | |
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| + | i.e., 68.3% of the area under a normal distribution is contained within one standard deviation of the mean. | ||
| − | + | :[[image:CumNormalGraph.png]] | |
| + | == See Also == | ||
* [[CumNormalInv]] -- the inverse cumulative density | * [[CumNormalInv]] -- the inverse cumulative density | ||
* [[Normal]] -- The normal distribution | * [[Normal]] -- The normal distribution | ||
* [[Erf]] -- The closely related error function | * [[Erf]] -- The closely related error function | ||
* [[Sigmoid]](x) -- Another sigmoidal-shaped function | * [[Sigmoid]](x) -- Another sigmoidal-shaped function | ||
Revision as of 21:17, 27 January 2016
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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