A Davidian curve defines a seminonparametric density, whose shape and flexibility can be tuned by
easy to estimate parameters. Since a special case of a Davidian curve is the standard normal density,
Davidian curves can be used for relaxing normality assumption in statistical applications (Zhang & Davidian, 2001)

A Davidian curve defines a seminonparametric density, whose shape and flexibility can be tuned by easy to estimate parameters. Since a special case of a Davidian curve is the standard normal density, Davidian curves can be used for relaxing normality assumption in statistical applications [1].

This package provides the density function, the gradient of the loglikelihood and a random generator for Davidian curves:

`ddc(x, phi)`

, Davidian curve density function`rdc(n, phi)`

, a random sampler for Davidian curves`dc_grad(x, phi)`

, the gradient function of Davidian curves

The second argument `phi`

of these functions is a vector, which contains the parameter(s) of a Davidian curve. The higher the number of parameters, the more flexible the density. The values of the parameres define the shape of the curve. Following [1, 2], this package provides support for Davidian curves up to 10 parameters.

- Zhang, D., & Davidian, M. (2001). Linear mixed models with flexible distributions of random effects for longitudinal data.
*Biometrics, 57*(3), 795-802. - Woods, C. M., & Lin, N. (2009). Item response theory with estimation of the latent density using Davidian curves.
*Applied Psychological Measurement, 33*(2), 102-117.

- Approximate values in M matrix are replaced with analytically obtained values (#9). Relevant code is reorganized.
- Bounds for Davidian curve parameters are removed. Thanks to R. Philip Chalmers for suggestions on this point.

- Initial release.
- Thanks to Carol M. Woods for kindly answering my questions prior to this release.