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circular (version 0.5-1)

Carthwrite: Carthwrite's Power-of-Cosine Density Function

Description

Density for the Carthwrite's power-of-cosine distribution.

Usage

dcarthwrite(x, mu, psi)

Value

The density

Arguments

x

a vector. The x and q objects are coerced to class circular.

mu

the location angular parameter. The object is coerced to class circular.

psi

the positive shape parameter.

Author

Federico Rotolo

Details

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 \(0 \le x < 2\pi\).

References

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.