The truncated normal distribution is the conditional distribution of a normally distributed random
variable restricted to an interval. If 
has a normal distribution
with mean 
and standard deviation 
, then the density of 
conditioned on 
is
![f(x)=(phi[(x-mu)/sigma])/(sigma[Phi[(b-mu)/sigma]-Phi[(a-mu)/sigma]]),](/images/equations/TruncatedNormalDistribution/NumberedEquation1.svg) |
for 
,
and is zero otherwise. Here 
and 
are the standard normal probability
density function and distribution function,
respectively. Either endpoint may be infinite, giving one-sided truncation.
