Truncated normal distribution

In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable by bounding the random variable from either below or above (or both). The truncated normal distribution has wide applications in statistics and econometrics. For example, it is used to model the probabilities of the binary outcomes in the probit model and to model censored data in the Tobit model. In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable by bounding the random variable from either below or above (or both). The truncated normal distribution has wide applications in statistics and econometrics. For example, it is used to model the probabilities of the binary outcomes in the probit model and to model censored data in the Tobit model. Suppose X {displaystyle X} has a normal distribution with mean μ {displaystyle mu } and variance σ 2 {displaystyle sigma ^{2}} and lies within the interval ( a , b ) , with − ∞ ≤ a < b ≤ ∞ {displaystyle (a,b),{ ext{with}};-infty leq a<bleq infty } . Then X {displaystyle X} conditional on a < X < b {displaystyle a<X<b} has a truncated normal distribution. Its probability density function, f {displaystyle f} , for a ≤ x ≤ b {displaystyle aleq xleq b} , is given by and by f = 0 {displaystyle f=0} otherwise.