On the Cartwright Power-of-Cosine Circular Distribution CPC- Some Distributional Properties and Characterizations

Abstract

For modelling the directional spectra of ocean waves, Cartwright introduced a power-of-cosine circular distribution, (cf. Cartwright, D. E. (1963), “The use of directional spectra in studying the output of a wave recorder on a moving ship, In Ocean Wave Spectra”, pages 203—218, Prentice Hall, New Jersey). Some distributional properties of the Cartwright’s power-of-cosine circular distribution will be discussed in this paper. Based on these properties, some characterizations of this distribution will be given using the truncated moment, order statistics and record values.