An Overview About Truncated Normal Distribution (R Code Included)

Source: MathWorks

First, let’s take a look at the definition from Wikipedia:

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.

Definition and features

A truncated normal distribution can be written as

Here the first two parameters are defined from a general normal distribution:

• The interval (a, b) is the truncated interval. The probability density function can be written as:

• The cumulated distribution function is:

• The inverse of cumulated distribution…