Suppose a herpetologist observes sea turtles emerging from the surf to
locate nesting sites. Since the landing site can be thought of as a
straight line, the directions from which the turtles arrive are confined to
a 180° arc. Similarly, an ornithologist observing the departure of sea birds
form the sheer face of a cliff need only record angles from within [0, ¼]
radians.
Classical statistical distributions that model angular data, such as the von
Mises, are designed for situations where a full 360° of observations might
occur. TAMU-CC statistician Dr. Jose Guardiola and his collaborators have
developed a new family of distributions specifically for semicircular data.
The new distribution is constructed by projecting the support of a normal
density onto a semicircle. We shall call this the semicircular normal (SCN)
family of distributions. This new family of distributions is simpler than
other families for angular data, more flexible in application, can be
extended to bimodal forms and to the full circle, and is particularly adept
as a model for axial data.
Suppose a herpetologist observes sea turtles emerging from the surf to
locate nesting sites. Since the landing site can be thought of as a 
We shall call this the semicircular normal (SCN)
family of distributions. This new family of distributions is simpler than
other families for angular data, more flexible in application, can be
extended to bimodal forms and to the full circle, and is particularly adept
as a model for axial data. 