Density for the Carthwrite's power-of-cosine distribution.
dcarthwrite(x, mu, psi)a vector. The x and q objects are coerced to class circular.
the location angular parameter. The object is coerced to class circular.
the positive shape parameter.
The density
The Carthwrite's power-of-cosine distribution has density $$ f(x)=\frac{2^{(1/\psi)-1} \Gamma^2((1/\psi)+1) (1+\cos(x-\mu))^{1/\psi}} {\pi\Gamma((2/\psi)+1)}, $$ for \(0 \le x < 2\pi\).
Carthwrite, D.E. (1963). The use of directional spectra in studying the output of a wave recorder on a moving ship. Ocean Wave Spectra , 203-218.