where the value of the summand is taken to be zero when , is the scale factor and is the location parameter. Expressing the above pdf in terms of the characteristic function of the Lévy distribution yields:
In terms of the circular variable the circular moments of the wrapped Lévy distribution are the characteristic function of the Lévy distribution evaluated at integer arguments:
where is some interval of length . The first moment is then the expectation value of z, also known as the mean resultant, or mean resultant vector: