CumNormal

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.

Library

Advanced math

See Also

• CumNormalInv -- the inverse cumulative density
• Normal -- The normal distribution
• Erf -- The closely related error function
• Sigmoid(x) -- Another sigmoidal-shaped function