Abstract
A new power normal family has been introduced by Isogai (1999) to transform a skewed and positive-valued distribution to a normal one. Its properties are shown compared to those of the Box and Cox's (1964) power normal family. Our new power normal family has many applications, because it includes not only log-normal and Weibull distributions but also the extreme value distribution of Type 2. However, the above two power normal families have a serious defect that they can treat positive-valued observations only. Thus, an alternative power normal family is constructed through our power normal family to deal with data comprised of positive- and negative-valued observations, and its properties are examined.
