A new class of distributions on the positive real line transformable to a Normal distibution

Music City Center 

Let X be a positive random variable with support on the positive real line. The log normal distribution for X is an example of transformation giving us Normal distribution. Technically, ln(X) is normally distributed. So we want to develop a class of 3 parameter distributions on the positive real line that can be transformed into a normal distribution. The transformation we want to consider is the Box-Cox transformation. It was shown no Box-Cox transformation of X can be normally distributed. By modifying the Box-Cox transformation slightly, we show that our new class of distributions is a transformable into a Normal distribution. In addition, we examine several properties of the new class of distributions algebraically and graphically.

Box - Cox transformations

Log normal distribution

Survival Analysis 

Biometrics Section