 Its probability density function, formula_7, for formula_8, is given by

and by formula_10 otherwise.Here,
is the probability density function of the standard normal distribution and formula_12 is its cumulative distribution function
By definition, if formula_14, then formula_15, and similarly, if formula_16, then formula_17.The above formulae show that when -\infty the scale parameter formula_3 of the truncated normal distribution is allowed to assume negative values.