Wrapped hb-skewed laplace distribution and its application in meteorology

Circular or directional data arise in different ways. The two main ways correspond to the two principal circular measuring instruments, the compass and the clock. Typical observations measured by the compass include wind directions and directions of migrating birds. Data of a similar type arise from measurements by spirit level or protractor. Typical observations measured by the clock include the arrival times (on a 24-hour clock) of patients at a casualty unit in a hospital. Data of a similar type arise as times of year or times of month of appropriate events. A circular observation can be regarded as a point on a circle of unit radius, or a unit vector (i.e. a direction) in the plane. Once an initial direction and an orientation of the circle have been chosen, each circular observation can be specified by the angle from the initial direction to the point on the circle corresponding to the observation.