Normal Distributions
Probability Density Function
The probability density function of a normal distribution is given by:
where:
is the mean of the distribution
is the standard deviation
See https://github.com/gbmhunter/BlogAssets/tree/master/Mathematics/Statistics/NormalDistribution for the code which generated these graphs.
Capped Normal Distribution
where:
is the standard deviation of the capped distribution
is the standard deviation of the normal distribution tails, ignoring the flat section in the middle
is the half-width of the flat section of the capped distribution
is the random variable